Load packages

library(tidyverse)
library(tidymodels)
library(janitor)
library(skimr)
library(kableExtra)
library(GGally)
library(vip)        
library(fastshap)   
library(MASS)
library(ISLR)
library(tree)
library(ggplot2)
library(dplyr)
library(lubridate)
library(imputeTS)
library(forecast)
library(urca)
library(pracma)
library(astsa)
library(fpp2)
library(imputeMissings)

Load data with read_csv()

turbine1 <- read_csv("/Users/ceciliadong/Desktop/Forcasting/Final Group Project/Turbine_Data.csv") %>%
  clean_names()
#data transformation
turbine1$date <- as.Date(turbine1$date)
head(turbine1) 
## # A tibble: 6 × 8
##    year month   day date       active_power ambient_temperature wind_d…¹ wind_…²
##   <dbl> <dbl> <dbl> <date>            <dbl>               <dbl>    <dbl>   <dbl>
## 1  2017    12    31 2017-12-31           NA                  NA       NA      NA
## 2  2017    12    31 2017-12-31           NA                  NA       NA      NA
## 3  2017    12    31 2017-12-31           NA                  NA       NA      NA
## 4  2017    12    31 2017-12-31           NA                  NA       NA      NA
## 5  2017    12    31 2017-12-31           NA                  NA       NA      NA
## 6  2017    12    31 2017-12-31           NA                  NA       NA      NA
## # … with abbreviated variable names ¹​wind_direction, ²​wind_speed
unique(turbine1$year)
## [1] 2017 2018 2019 2020
#since we need to provide daily forecast for 2020, we can merely select the data in 2019 and 2020 to do forecast

turbine <- turbine1 %>% 
  filter(year == 2020 | year == 2019 | year == 2018)
head(turbine)
## # A tibble: 6 × 8
##    year month   day date       active_power ambient_temperature wind_d…¹ wind_…²
##   <dbl> <dbl> <dbl> <date>            <dbl>               <dbl>    <dbl>   <dbl>
## 1  2018     1     1 2018-01-01        -5.36                23.1       8     2.28
## 2  2018     1     1 2018-01-01        -5.82                23.0     300.    2.34
## 3  2018     1     1 2018-01-01        -5.28                22.9     340     2.46
## 4  2018     1     1 2018-01-01        -4.65                23.0     345     2.03
## 5  2018     1     1 2018-01-01        -4.68                22.9     345     1.83
## 6  2018     1     1 2018-01-01        -4.76                22.9     345     1.65
## # … with abbreviated variable names ¹​wind_direction, ²​wind_speed
tail(turbine)
## # A tibble: 6 × 8
##    year month   day date       active_power ambient_temperature wind_d…¹ wind_…²
##   <dbl> <dbl> <dbl> <date>            <dbl>               <dbl>    <dbl>   <dbl>
## 1  2020     3    30 2020-03-30         90.3                27.6      178    3.61
## 2  2020     3    30 2020-03-30         70.0                27.5      178    3.53
## 3  2020     3    30 2020-03-30         40.8                27.6      178    3.26
## 4  2020     3    30 2020-03-30         20.8                27.6      178    3.33
## 5  2020     3    30 2020-03-30         62.1                27.8      190    3.28
## 6  2020     3    30 2020-03-30         68.7                27.9      203    3.48
## # … with abbreviated variable names ¹​wind_direction, ²​wind_speed

Looking at Data quaility

skim(turbine)
Data summary
Name turbine
Number of rows 118080
Number of columns 8
_______________________
Column type frequency:
Date 1
numeric 7
________________________
Group variables None

Variable type: Date

skim_variable n_missing complete_rate min max median n_unique
date 0 1 2018-01-01 2020-03-30 2019-02-14 820

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
year 0 1.00 2018.66 0.67 2018.00 2018.00 2019.00 2019.00 2020.00 ▇▁▇▁▂
month 0 1.00 6.03 3.56 1.00 3.00 6.00 9.00 12.00 ▇▃▃▃▆
day 0 1.00 15.70 8.78 1.00 8.00 16.00 23.00 31.00 ▇▇▇▇▆
active_power 23330 0.80 619.11 611.28 -38.52 79.64 402.65 1074.59 1779.03 ▇▃▂▁▃
ambient_temperature 24263 0.79 28.77 4.37 0.00 25.63 28.34 31.66 42.41 ▁▁▃▇▂
wind_direction 45802 0.61 196.29 88.30 0.00 145.00 182.00 271.00 357.00 ▁▃▇▃▅
wind_speed 23485 0.80 5.88 2.62 0.00 3.82 5.56 7.51 22.97 ▅▇▂▁▁
#missing data in active_power, ambient_temperature, wind_direction, wind_speed

Accumulate Using a daily index and plot the tine series

turbine_clean <- turbine %>%
  na_interpolation()

day_turbine1 <- turbine_clean %>%
  group_by(year, month, day) %>%
  summarize(active_power = sum(active_power),ambient_temperature = mean(ambient_temperature),
            wind_direction=mean(wind_direction), wind_speed=mean(wind_speed))


head(day_turbine1)
## # A tibble: 6 × 7
## # Groups:   year, month [1]
##    year month   day active_power ambient_temperature wind_direction wind_speed
##   <dbl> <dbl> <dbl>        <dbl>               <dbl>          <dbl>      <dbl>
## 1  2018     1     1       27571.                26.5           282.       3.88
## 2  2018     1     2       48502.                25.6           273.       4.67
## 3  2018     1     3       45905.                25.5           276.       4.53
## 4  2018     1     4       51965.                24.9           285.       5.06
## 5  2018     1     5       34609.                24.6           281.       4.42
## 6  2018     1     6       19548.                22.6           312.       3.81
#drop everything but the series
day_turbine <- subset(day_turbine1, select = -c(year,month,day, ambient_temperature, wind_direction, wind_speed))
head(day_turbine)
## # A tibble: 6 × 1
##   active_power
##          <dbl>
## 1       27571.
## 2       48502.
## 3       45905.
## 4       51965.
## 5       34609.
## 6       19548.
## Create a daily Date object - helps my work on dates                                              
inds <- seq(as.Date("2020-01-01"), as.Date("2020-03-30"), by = "day")

as.numeric(format(inds[1], "%j"))
## [1] 1
## Create a time series object
turbine_ts <- ts(day_turbine, start=c(2018,1), frequency = 365)

plot(turbine_ts)

turbine_tsi <- na_interpolation(turbine_ts)
print(turbine_tsi)
## Time Series:
## Start = c(2018, 1) 
## End = c(2020, 90) 
## Frequency = 365 
##        active_power
##   [1,]   27570.7490
##   [2,]   48501.8066
##   [3,]   45904.8192
##   [4,]   51965.3897
##   [5,]   34608.7212
##   [6,]   19547.6142
##   [7,]   51213.1585
##   [8,]  109448.1129
##   [9,]   73036.1857
##  [10,]   63902.4295
##  [11,]   61334.3685
##  [12,]   22953.0853
##  [13,]   51947.0029
##  [14,]   78659.0128
##  [15,]   28028.4875
##  [16,]   57517.5491
##  [17,]   58322.8032
##  [18,]   62372.4582
##  [19,]   52478.7977
##  [20,]   32712.2594
##  [21,]   68070.9847
##  [22,]   54241.9801
##  [23,]     575.8896
##  [24,]   19003.0921
##  [25,]   35369.2910
##  [26,]   27638.6489
##  [27,]   37203.0604
##  [28,]   89179.6072
##  [29,]   68457.4715
##  [30,]   64474.1900
##  [31,]   60490.9085
##  [32,]   56507.6271
##  [33,]   52524.3456
##  [34,]   48541.0641
##  [35,]   44557.7826
##  [36,]   82866.0597
##  [37,]   27091.2670
##  [38,]     323.2630
##  [39,]    -806.0467
##  [40,]   24529.5492
##  [41,]   74559.3573
##  [42,]  145699.8866
##  [43,]  107534.0413
##  [44,]  102250.9333
##  [45,]  110567.3547
##  [46,]   68428.7233
##  [47,]   24990.6226
##  [48,]   29073.9695
##  [49,]   69059.6228
##  [50,]   81140.3567
##  [51,]   65055.2261
##  [52,]   72437.6783
##  [53,]   66946.9888
##  [54,]  107783.5803
##  [55,]   95825.6784
##  [56,]   60335.7075
##  [57,]   53813.5629
##  [58,]   74436.3577
##  [59,]   44693.4339
##  [60,]   71899.0337
##  [61,]   77251.5493
##  [62,]   81959.6535
##  [63,]   83585.4457
##  [64,]    3798.5657
##  [65,]   12830.1507
##  [66,]   21861.7357
##  [67,]   30893.3208
##  [68,]   39924.9058
##  [69,]   48956.4909
##  [70,]   57988.0759
##  [71,]  102753.6762
##  [72,]   53503.7587
##  [73,]   71493.8184
##  [74,]   69758.6555
##  [75,]   16872.8845
##  [76,]   56915.2956
##  [77,]   34638.3958
##  [78,]   64342.0376
##  [79,]    5007.0803
##  [80,]   30554.1082
##  [81,]   58212.6157
##  [82,]   85871.1232
##  [83,]  113529.6307
##  [84,]  112259.3407
##  [85,]   70367.3271
##  [86,]   51506.6464
##  [87,]   44817.3289
##  [88,]   44734.6538
##  [89,]   77495.3463
##  [90,]   44537.6007
##  [91,]   73943.3063
##  [92,]   52573.3614
##  [93,]   18622.2044
##  [94,]   51126.8017
##  [95,]   37440.7316
##  [96,]   42863.9081
##  [97,]   56981.5834
##  [98,]   49086.2151
##  [99,]   20472.2727
## [100,]   17292.9787
## [101,]   14113.6847
## [102,]   10934.3908
## [103,]    7755.0968
## [104,]    4575.8028
## [105,]    1396.5088
## [106,]   42468.9836
## [107,]   40874.2498
## [108,]   32343.9749
## [109,]   43493.7989
## [110,]   65679.3857
## [111,]   23462.2087
## [112,]   29459.2574
## [113,]   23963.9104
## [114,]  107572.2068
## [115,]   44247.2459
## [116,]   49588.6874
## [117,]   67219.0132
## [118,]   40363.4854
## [119,]   43972.9401
## [120,]   72157.9228
## [121,]   92179.3082
## [122,]   67172.5549
## [123,]   25232.8920
## [124,]    4546.3935
## [125,]    9413.9076
## [126,]   14281.4218
## [127,]   19148.9360
## [128,]   43641.5834
## [129,]   30986.1764
## [130,]   45511.6414
## [131,]   11605.3728
## [132,]   39050.5848
## [133,]  165284.0346
## [134,]  247033.8136
## [135,]  242759.1490
## [136,]  238484.4844
## [137,]  234209.8199
## [138,]  229935.1553
## [139,]  225660.4908
## [140,]  221385.8262
## [141,]   49060.6481
## [142,]   23515.6774
## [143,]    5118.3943
## [144,]   23993.0843
## [145,]   44549.0676
## [146,]   55953.1316
## [147,]   42845.4939
## [148,]   30754.7468
## [149,]  115720.2796
## [150,]  108829.1860
## [151,]   72605.8510
## [152,]   36768.1062
## [153,]   63570.3009
## [154,]   91402.5586
## [155,]  108365.7473
## [156,]   83526.9359
## [157,]  148429.5740
## [158,]  142197.6523
## [159,]  179853.3806
## [160,]  231335.0031
## [161,]  245379.0967
## [162,]  243516.2585
## [163,]  247259.4132
## [164,]  188305.4173
## [165,]  180869.6587
## [166,]  121730.6821
## [167,]  184069.1088
## [168,]  245489.5216
## [169,]  224632.3925
## [170,]  215787.6876
## [171,]  206942.9827
## [172,]  198098.2778
## [173,]  189253.5730
## [174,]  180408.8681
## [175,]  171564.1632
## [176,]  216989.6747
## [177,]  243026.1138
## [178,]  211952.7119
## [179,]  128864.9539
## [180,]   88258.9426
## [181,]   71793.2951
## [182,]   68023.5798
## [183,]  142042.4227
## [184,]  167034.4919
## [185,]  227756.8367
## [186,]  237900.6917
## [187,]  233659.1968
## [188,]  192333.7806
## [189,]  155859.3234
## [190,]  209426.1381
## [191,]  235391.5593
## [192,]  241748.3964
## [193,]  247463.2193
## [194,]  236414.3548
## [195,]  246811.2376
## [196,]  247703.7808
## [197,]  241294.5209
## [198,]  242778.1402
## [199,]  240281.1134
## [200,]  246399.2187
## [201,]  247547.6838
## [202,]  245052.8500
## [203,]  242054.8788
## [204,]  247603.3109
## [205,]  247578.5656
## [206,]  247553.8203
## [207,]  247529.0750
## [208,]  247504.3296
## [209,]  247479.5843
## [210,]  247454.8390
## [211,]  225930.9632
## [212,]  232351.4143
## [213,]  229839.4262
## [214,]  240940.8227
## [215,]  169535.2878
## [216,]  241925.3668
## [217,]  243253.2495
## [218,]  229944.6655
## [219,]  237335.8393
## [220,]  175328.7696
## [221,]  203241.8244
## [222,]  243650.7685
## [223,]  224281.6308
## [224,]  243223.1839
## [225,]  218881.3460
## [226,]  187799.3771
## [227,]  220802.0974
## [228,]   91753.7250
## [229,]  202811.3419
## [230,]  212584.7445
## [231,]  247610.2400
## [232,]  247545.8523
## [233,]  239950.3676
## [234,]  237783.4274
## [235,]  234589.1171
## [236,]  159488.0631
## [237,]  218692.2798
## [238,]  227459.8361
## [239,]  199517.7323
## [240,]  226803.0565
## [241,]  174376.7993
## [242,]  182528.1054
## [243,]  204773.7394
## [244,]  154552.9836
## [245,]  164553.9773
## [246,]  141173.1967
## [247,]  137460.3018
## [248,]  170791.5186
## [249,]  212163.8263
## [250,]  225936.4259
## [251,]  120628.0534
## [252,]   27514.4747
## [253,]   17082.8538
## [254,]   43627.7239
## [255,]   22388.7219
## [256,]   36870.3405
## [257,]   31962.8997
## [258,]   71513.5640
## [259,]   73754.4642
## [260,]   80117.7269
## [261,]   86010.6810
## [262,]   94760.5933
## [263,]   81034.5081
## [264,]  107514.9495
## [265,]    9204.7444
## [266,]   30025.0052
## [267,]    6735.3657
## [268,]    8257.4834
## [269,]   44382.8933
## [270,]   50499.8310
## [271,]   45298.4298
## [272,]   26750.3233
## [273,]   42379.7475
## [274,]   74618.1331
## [275,]   40283.1587
## [276,]   20703.9128
## [277,]   23506.8566
## [278,]   50965.0600
## [279,]   77192.4442
## [280,]   60161.4854
## [281,]   38665.8374
## [282,]   29984.1873
## [283,]   63693.5980
## [284,]   81011.9923
## [285,]   25115.3500
## [286,]   27249.5238
## [287,]   27853.1519
## [288,]   61182.5106
## [289,]   40115.6559
## [290,]   32087.4159
## [291,]   20601.0896
## [292,]   37200.5854
## [293,]   34558.9090
## [294,]   78479.2134
## [295,]   22369.7385
## [296,]   52859.5643
## [297,]   51181.6004
## [298,]   70214.7184
## [299,]   53915.9674
## [300,]   49207.6785
## [301,]   39830.3759
## [302,]    1806.2227
## [303,]   26463.8415
## [304,]   76569.7118
## [305,]   59738.6705
## [306,]   54506.0523
## [307,]   71607.2006
## [308,]  128636.1926
## [309,]   62882.7208
## [310,]   48956.8243
## [311,]   86654.1952
## [312,]   69301.5996
## [313,]   37584.2293
## [314,]   21998.5391
## [315,]   16341.0962
## [316,]   34084.4727
## [317,]   13956.0862
## [318,]   24819.2236
## [319,]   95141.2307
## [320,]   50068.4832
## [321,]   57244.6707
## [322,]   96518.0097
## [323,]  101593.5913
## [324,]   62445.3142
## [325,]   55813.8473
## [326,]   73680.4467
## [327,]   63066.7539
## [328,]   80538.9412
## [329,]   48076.9329
## [330,]   53593.9903
## [331,]   64209.4654
## [332,]   38489.1916
## [333,]   21776.7627
## [334,]   22571.3329
## [335,]   21779.7076
## [336,]   55565.1584
## [337,]   65718.5403
## [338,]   59931.3096
## [339,]   68945.7748
## [340,]   69243.2214
## [341,]   53286.1693
## [342,]   74325.7021
## [343,]   70929.4476
## [344,]   44521.7921
## [345,]   60582.5536
## [346,]   58355.9437
## [347,]   64335.2023
## [348,]   72616.0246
## [349,]  104044.4232
## [350,]   14032.5465
## [351,]   64990.1447
## [352,]   55079.9099
## [353,]   33494.9636
## [354,]   63026.1350
## [355,]   43332.7666
## [356,]   43140.3845
## [357,]   73988.3087
## [358,]   56912.1287
## [359,]   44246.4313
## [360,]   48116.0382
## [361,]   34229.2141
## [362,]   60421.5896
## [363,]   73453.3299
## [364,]   53194.5831
## [365,]   44923.3967
## [366,]   63162.2187
## [367,]   57652.3635
## [368,]   48618.2301
## [369,]   76921.6673
## [370,]   88400.8941
## [371,]   93094.6176
## [372,]   49323.7084
## [373,]   39487.3785
## [374,]   78088.8084
## [375,]  109774.9036
## [376,]   73567.2134
## [377,]  101537.7076
## [378,]   76258.6681
## [379,]   74350.3923
## [380,]   54109.5095
## [381,]   45187.6888
## [382,]   67572.7283
## [383,]   41221.8908
## [384,]   37870.5457
## [385,]   54982.6668
## [386,]   95915.5172
## [387,]   72962.1173
## [388,]   48462.0036
## [389,]   59127.2137
## [390,]   89946.0758
## [391,]  159883.6761
## [392,]  110484.3315
## [393,]   51935.9051
## [394,]   44886.9482
## [395,]   56152.8766
## [396,]  113533.8948
## [397,]   64865.2445
## [398,]   48439.6483
## [399,]   93499.6985
## [400,]  110844.2061
## [401,]   95351.8594
## [402,]   78058.3078
## [403,]   57446.4310
## [404,]   42410.4212
## [405,]   65399.3116
## [406,]  125900.6835
## [407,]  166116.6614
## [408,]  119365.6472
## [409,]   80715.9681
## [410,]  109475.7097
## [411,]   44000.0354
## [412,]   28590.9532
## [413,]   16658.7355
## [414,]   35053.8109
## [415,]  103065.4975
## [416,]  113371.8209
## [417,]   80293.5981
## [418,]   94212.8378
## [419,]   76841.7081
## [420,]   84032.7813
## [421,]   49992.6958
## [422,]   28397.0704
## [423,]   14327.9237
## [424,]   50943.6773
## [425,]   86653.1134
## [426,]  125397.1291
## [427,]   27478.7215
## [428,]   39004.9787
## [429,]   40393.6875
## [430,]   58523.0716
## [431,]   47463.5458
## [432,]   66043.2863
## [433,]   45326.3874
## [434,]   37030.1886
## [435,]   49205.6785
## [436,]   56770.8072
## [437,]   56898.4150
## [438,]   85766.1997
## [439,]   98497.1187
## [440,]  135351.0203
## [441,]   80687.8039
## [442,]   91516.8657
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## [451,]   69979.2500
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## [783,]  113207.3812
## [784,]   71293.1174
## [785,]   69622.9442
## [786,]   50851.3427
## [787,]   67775.2191
## [788,]   73532.5681
## [789,]   90140.0199
## [790,]   67270.0487
## [791,]   54483.4662
## [792,]   37944.8557
## [793,]   25511.0286
## [794,]    7283.2261
## [795,]   33941.2305
## [796,]   37421.9037
## [797,]   67601.4039
## [798,]   77277.9714
## [799,]   77932.1601
## [800,]   71391.2921
## [801,]   45396.3431
## [802,]   50925.9009
## [803,]   83584.3563
## [804,]   97495.2657
## [805,]   99893.3274
## [806,]   86356.4435
## [807,]  113210.0313
## [808,]   38362.0458
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## [811,]   40735.6793
## [812,]   45381.0955
## [813,]   74485.0385
## [814,]   56555.0813
## [815,]   86550.6953
## [816,]   92876.9967
## [817,]  103492.1290
## [818,]   95972.5666
## [819,]  114258.5268
## [820,]  105566.5782
plot(turbine_tsi)

Test original series for stationary

Box.test(turbine_tsi, lag=8, fitdf=0, type="Lj")
## 
##  Box-Ljung test
## 
## data:  turbine_tsi
## X-squared = 3437, df = 8, p-value < 2.2e-16
#Ho: white noise
#Ha: not white noise
#p value < 0.05, reject Ho, the original turbine_ts series is not white noise, so we need to build model for it

Plot ACF and PACF for turbine and test for stationary

plot(turbine_tsi)

ggAcf(turbine_tsi)

#ACF quickly decays to 0
ggPacf(turbine_tsi)

#lag 1 is positive in PACF, suggesting autoregression

#test for stationary
turbine_df <- ur.df(turbine_tsi, type = "drift")
summary(turbine_df)
## 
## ############################################### 
## # Augmented Dickey-Fuller Test Unit Root Test # 
## ############################################### 
## 
## Test regression drift 
## 
## 
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -159375  -19053    -292   17268  123299 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 9222.39368 1821.86442   5.062 5.13e-07 ***
## z.lag.1       -0.10080    0.01597  -6.312 4.52e-10 ***
## z.diff.lag    -0.03374    0.03499  -0.964    0.335    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 31600 on 815 degrees of freedom
## Multiple R-squared:  0.05333,    Adjusted R-squared:  0.051 
## F-statistic: 22.96 on 2 and 815 DF,  p-value: 2.002e-10
## 
## 
## Value of test-statistic is: -6.312 19.9232 
## 
## Critical values for test statistics: 
##       1pct  5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1  6.43  4.59  3.78
#H0:nonstationary and needs a 1st difference
#Ha: Stationary (does not need a first diff)
#p value of z.lag.1 is less than 0.05, reject Ho, series turbine_tsi is stationary, d = 0

Fit Simple ESM Model

turbine_esm <- ses(turbine_tsi, h=5)
summary(turbine_esm)
## 
## Forecast method: Simple exponential smoothing
## 
## Model Information:
## Simple exponential smoothing 
## 
## Call:
##  ses(y = turbine_tsi, h = 5) 
## 
##   Smoothing parameters:
##     alpha = 0.885 
## 
##   Initial states:
##     l = 30061.9863 
## 
##   sigma:  32271.66
## 
##      AIC     AICc      BIC 
## 22532.02 22532.05 22546.14 
## 
## Error measures:
##                    ME     RMSE      MAE  MPE MAPE      MASE       ACF1
## Training set 105.1025 32232.28 23325.22 -Inf  Inf 0.5365042 0.01590287
## 
## Forecasts:
##           Point Forecast    Lo 80    Hi 80      Lo 95    Hi 95
## 2020.2466       106333.8 64975.97 147691.6  43082.472 169585.1
## 2020.2493       106333.8 51105.97 161561.6  21870.147 190797.4
## 2020.2521       106333.8 40078.57 172589.0   5005.193 207662.3
## 2020.2548       106333.8 30641.02 182026.5  -9428.303 222095.8
## 2020.2575       106333.8 22256.22 190411.3 -22251.744 234919.3
# RMSE = 32232.28, MAE = 23325.22, forecast errors are not decent

forecast(turbine_esm)
##           Point Forecast    Lo 80    Hi 80      Lo 95    Hi 95
## 2020.2466       106333.8 64975.97 147691.6  43082.472 169585.1
## 2020.2493       106333.8 51105.97 161561.6  21870.147 190797.4
## 2020.2521       106333.8 40078.57 172589.0   5005.193 207662.3
## 2020.2548       106333.8 30641.02 182026.5  -9428.303 222095.8
## 2020.2575       106333.8 22256.22 190411.3 -22251.744 234919.3
turbine_esm %>% forecast() %>% autoplot()

Try auto.arima

fit_auto <- auto.arima(turbine_tsi, xreg = as.matrix(day_turbine1[, 5:7]))
summary(fit_auto)
## Series: turbine_tsi 
## Regression with ARIMA(1,0,1) errors 
## 
## Coefficients:
##          ar1     ma1  intercept  ambient_temperature  wind_direction
##       0.7001  0.2075  -60012.68            -432.6182        -18.7551
## s.e.  0.0346  0.0465   11867.09             373.7633         16.3386
##       wind_speed
##       27984.5680
## s.e.    576.9068
## 
## sigma^2 = 259403820:  log likelihood = -9104.31
## AIC=18222.62   AICc=18222.76   BIC=18255.59
## 
## Training set error measures:
##                    ME     RMSE      MAE  MPE MAPE      MASE         ACF1
## Training set 3.655038 16046.99 10326.17 -Inf  Inf 0.2375126 -0.001151008
checkresiduals(fit_auto)

## 
##  Ljung-Box test
## 
## data:  Residuals from Regression with ARIMA(1,0,1) errors
## Q* = 251.67, df = 162, p-value = 8.019e-06
## 
## Model df: 2.   Total lags used: 164
#RMSE = 16046.99, MAE = 10326.17, better than using simple ESM model

fit1_auto <- sarima(turbine_tsi, 1, 0, 1,xreg = as.matrix(day_turbine1[, 5:7]))
## initial  value 10.126967 
## iter   2 value 9.932420
## iter   3 value 9.707907
## iter   4 value 9.701572
## iter   5 value 9.698732
## iter   6 value 9.687617
## iter   7 value 9.685632
## iter   8 value 9.684290
## iter   9 value 9.684031
## iter  10 value 9.683910
## iter  11 value 9.683904
## iter  12 value 9.683897
## iter  13 value 9.683887
## iter  14 value 9.683879
## iter  15 value 9.683878
## iter  16 value 9.683878
## iter  17 value 9.683877
## iter  18 value 9.683877
## iter  19 value 9.683876
## iter  20 value 9.683876
## iter  20 value 9.683876
## iter  20 value 9.683876
## final  value 9.683876 
## converged
## initial  value 9.683880 
## iter   2 value 9.683879
## iter   2 value 9.683879
## iter   2 value 9.683879
## final  value 9.683879 
## converged

fit1_auto
## $fit
## 
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, 
##     Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc, 
##     REPORT = 1, reltol = tol))
## 
## Coefficients:
##          ar1     ma1  intercept  ambient_temperature  wind_direction
##       0.7001  0.2075  -60012.68            -432.6182        -18.7551
## s.e.  0.0346  0.0465   11867.09             373.7633         16.3386
##       wind_speed
##       27984.5680
## s.e.    576.9068
## 
## sigma^2 estimated as 257505743:  log likelihood = -9104.31,  aic = 18222.62
## 
## $degrees_of_freedom
## [1] 814
## 
## $ttable
##                        Estimate         SE t.value p.value
## ar1                      0.7001     0.0346 20.2122  0.0000
## ma1                      0.2075     0.0465  4.4582  0.0000
## intercept           -60012.6769 11867.0865 -5.0571  0.0000
## ambient_temperature   -432.6182   373.7633 -1.1575  0.2474
## wind_direction         -18.7551    16.3386 -1.1479  0.2513
## wind_speed           27984.5680   576.9068 48.5080  0.0000
## 
## $AIC
## [1] 22.22271
## 
## $AICc
## [1] 22.22283
## 
## $BIC
## [1] 22.26291
#Residuals are not white noise; temperature and direction are not significant

#Not all the ACF are within the error bond, is not white noise
accuracy(fit_auto)
##                    ME     RMSE      MAE  MPE MAPE      MASE         ACF1
## Training set 3.655038 16046.99 10326.17 -Inf  Inf 0.2375126 -0.001151008
#fit_auto %>% forecast() %>% autoplot()


##create forecast and actual data line together, create overlap plot
#red line deviates from the balck peaks and bottoms
ts.plot(turbine_tsi, fitted(fit_auto), gpars=list(col=c("black","red")))

#seems resonable

Try intervention and iteratly select the best model

fit_AR1 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(1,0,1))
summary(fit_AR1)
## Series: turbine_tsi 
## Regression with ARIMA(1,0,1) errors 
## 
## Coefficients:
##          ar1     ma1  intercept      xreg
##       0.7011  0.2035  -75857.82  27932.79
## s.e.  0.0341  0.0463    4098.91    574.53
## 
## sigma^2 = 259637818:  log likelihood = -9105.68
## AIC=18221.37   AICc=18221.44   BIC=18244.92
## 
## Training set error measures:
##                    ME     RMSE      MAE  MPE MAPE      MASE          ACF1
## Training set 7.072441 16073.93 10296.59 -Inf  Inf 0.2368323 -0.0006827484
checkresiduals(fit_AR1)

## 
##  Ljung-Box test
## 
## data:  Residuals from Regression with ARIMA(1,0,1) errors
## Q* = 253.13, df = 162, p-value = 6.078e-06
## 
## Model df: 2.   Total lags used: 164
#RMSE = 16073.93, MAE = 10296.59
fit1_AR <- sarima(turbine_tsi, 1, 0, 1,xreg = day_turbine1$wind_speed)
## initial  value 10.135842 
## iter   2 value 9.942492
## iter   3 value 9.706225
## iter   4 value 9.700462
## iter   5 value 9.697852
## iter   6 value 9.691525
## iter   7 value 9.688465
## iter   8 value 9.686646
## iter   9 value 9.685844
## iter  10 value 9.685614
## iter  11 value 9.685577
## iter  12 value 9.685551
## iter  13 value 9.685548
## iter  14 value 9.685547
## iter  14 value 9.685547
## iter  14 value 9.685547
## final  value 9.685547 
## converged
## initial  value 9.685557 
## iter   2 value 9.685556
## iter   3 value 9.685556
## iter   4 value 9.685555
## iter   5 value 9.685555
## iter   5 value 9.685555
## iter   5 value 9.685555
## final  value 9.685555 
## converged

fit1_AR
## $fit
## 
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, 
##     Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc, 
##     REPORT = 1, reltol = tol))
## 
## Coefficients:
##          ar1     ma1  intercept      xreg
##       0.7011  0.2035  -75857.82  27932.79
## s.e.  0.0341  0.0463    4098.91    574.53
## 
## sigma^2 estimated as 258371292:  log likelihood = -9105.68,  aic = 18221.37
## 
## $degrees_of_freedom
## [1] 816
## 
## $ttable
##              Estimate        SE  t.value p.value
## ar1            0.7011    0.0341  20.5423       0
## ma1            0.2035    0.0463   4.3908       0
## intercept -75857.8216 4098.9101 -18.5068       0
## xreg       27932.7931  574.5300  48.6185       0
## 
## $AIC
## [1] 22.22118
## 
## $AICc
## [1] 22.22124
## 
## $BIC
## [1] 22.2499
#All the terms are significant, residuals are not white noise; relatively high forecast error

fit_AR2 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(1,1,1))
summary(fit_AR2)
## Series: turbine_tsi 
## Regression with ARIMA(1,1,1) errors 
## 
## Coefficients:
##           ar1     ma1        xreg
##       -0.6622  0.7374  26709.0723
## s.e.   0.1150  0.1022    577.9466
## 
## sigma^2 = 293680665:  log likelihood = -9145.05
## AIC=18298.1   AICc=18298.15   BIC=18316.93
## 
## Training set error measures:
##                   ME     RMSE      MAE MPE MAPE      MASE        ACF1
## Training set 25.6462 17095.26 11094.76 NaN  Inf 0.2551909 -0.04550076
checkresiduals(fit_AR2)

## 
##  Ljung-Box test
## 
## data:  Residuals from Regression with ARIMA(1,1,1) errors
## Q* = 263.36, df = 162, p-value = 8.19e-07
## 
## Model df: 2.   Total lags used: 164
#RMSE = 17095.26, MAE = 11094.76
fit2_AR <- sarima(turbine_tsi, 1, 1, 1,xreg = day_turbine1$wind_speed)
## initial  value 9.752700 
## iter   2 value 9.752627
## iter   3 value 9.752545
## iter   4 value 9.752541
## iter   5 value 9.752315
## iter   6 value 9.751967
## iter   7 value 9.751760
## iter   8 value 9.751429
## iter   9 value 9.750927
## iter  10 value 9.749881
## iter  11 value 9.749806
## iter  12 value 9.749589
## iter  13 value 9.749237
## iter  14 value 9.748830
## iter  15 value 9.748505
## iter  16 value 9.748326
## iter  17 value 9.748106
## iter  18 value 9.747927
## iter  19 value 9.747861
## iter  20 value 9.747846
## iter  21 value 9.747832
## iter  22 value 9.747828
## iter  23 value 9.747821
## iter  24 value 9.747799
## iter  25 value 9.747787
## iter  26 value 9.747783
## iter  27 value 9.747782
## iter  28 value 9.747780
## iter  29 value 9.747779
## iter  30 value 9.747779
## iter  31 value 9.747778
## iter  32 value 9.747778
## iter  32 value 9.747778
## iter  32 value 9.747778
## final  value 9.747778 
## converged
## initial  value 9.747180 
## iter   1 value 9.747180
## final  value 9.747180 
## converged

fit2_AR
## $fit
## 
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, 
##     Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc, 
##     REPORT = 1, reltol = tol))
## 
## Coefficients:
##           ar1     ma1        xreg
##       -0.6622  0.7374  26709.0723
## s.e.   0.1150  0.1022    577.9466
## 
## sigma^2 estimated as 292604904:  log likelihood = -9145.05,  aic = 18298.1
## 
## $degrees_of_freedom
## [1] 816
## 
## $ttable
##        Estimate       SE t.value p.value
## ar1     -0.6622   0.1150 -5.7574       0
## ma1      0.7374   0.1022  7.2192       0
## xreg 26709.0723 577.9466 46.2137       0
## 
## $AIC
## [1] 22.34201
## 
## $AICc
## [1] 22.34204
## 
## $BIC
## [1] 22.365
#Residuals are not white noise; high forecast error

fit_AR4 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(3,1,1))
summary(fit_AR4)
## Series: turbine_tsi 
## Regression with ARIMA(3,1,1) errors 
## 
## Coefficients:
##          ar1      ar2      ar3      ma1        xreg
##       0.8594  -0.1616  -0.0171  -0.9605  27317.2767
## s.e.  0.0373   0.0459   0.0363   0.0132    588.7666
## 
## sigma^2 = 259510578:  log likelihood = -9094
## AIC=18199.99   AICc=18200.1   BIC=18228.24
## 
## Training set error measures:
##                    ME     RMSE      MAE  MPE MAPE      MASE        ACF1
## Training set 94.84751 16050.29 10314.68 -Inf  Inf 0.2372484 -0.00122635
checkresiduals(fit_AR4)

## 
##  Ljung-Box test
## 
## data:  Residuals from Regression with ARIMA(3,1,1) errors
## Q* = 229.39, df = 160, p-value = 0.0002662
## 
## Model df: 4.   Total lags used: 164
#RMSE = 16050.29, MAE = 10314.68
fit4_AR <- sarima(turbine_tsi, 3, 1, 1,xreg = day_turbine1$wind_speed)
## initial  value 9.753782 
## iter   2 value 9.740178
## iter   3 value 9.739763
## iter   4 value 9.739105
## iter   5 value 9.738675
## iter   6 value 9.734370
## iter   7 value 9.730971
## iter   8 value 9.717202
## iter   9 value 9.715762
## iter  10 value 9.697615
## iter  11 value 9.695909
## iter  12 value 9.694091
## iter  13 value 9.691296
## iter  14 value 9.688264
## iter  15 value 9.687930
## iter  16 value 9.687826
## iter  17 value 9.687655
## iter  18 value 9.687627
## iter  19 value 9.687611
## iter  20 value 9.687606
## iter  21 value 9.687605
## iter  21 value 9.687605
## iter  21 value 9.687605
## final  value 9.687605 
## converged
## initial  value 9.684970 
## iter   2 value 9.684938
## iter   3 value 9.684872
## iter   4 value 9.684854
## iter   5 value 9.684849
## iter   6 value 9.684846
## iter   7 value 9.684843
## iter   8 value 9.684843
## iter   8 value 9.684842
## iter   8 value 9.684842
## final  value 9.684842 
## converged

fit4_AR
## $fit
## 
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, 
##     Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc, 
##     REPORT = 1, reltol = tol))
## 
## Coefficients:
##          ar1      ar2      ar3      ma1        xreg
##       0.8594  -0.1616  -0.0171  -0.9605  27317.2767
## s.e.  0.0373   0.0459   0.0363   0.0132    588.7666
## 
## sigma^2 estimated as 257926257:  log likelihood = -9094,  aic = 18199.99
## 
## $degrees_of_freedom
## [1] 814
## 
## $ttable
##        Estimate       SE  t.value p.value
## ar1      0.8594   0.0373  23.0210  0.0000
## ar2     -0.1616   0.0459  -3.5247  0.0004
## ar3     -0.0171   0.0363  -0.4704  0.6382
## ma1     -0.9605   0.0132 -72.9282  0.0000
## xreg 27317.2767 588.7666  46.3975  0.0000
## 
## $AIC
## [1] 22.22221
## 
## $AICc
## [1] 22.2223
## 
## $BIC
## [1] 22.25671
#Residuals are not white noise; ar3 is not significant

fit_AR5 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(2,1,2))
summary(fit_AR5)
## Series: turbine_tsi 
## Regression with ARIMA(2,1,2) errors 
## 
## Coefficients:
##          ar1     ar2      ma1      ma2        xreg
##       0.3350  0.2391  -0.4383  -0.5143  27315.5935
## s.e.  0.2129  0.1734   0.2009   0.1979    589.4629
## 
## sigma^2 = 259801848:  log likelihood = -9094.47
## AIC=18200.93   AICc=18201.04   BIC=18229.18
## 
## Training set error measures:
##                    ME     RMSE      MAE  MPE MAPE      MASE       ACF1
## Training set 95.62227 16059.29 10298.89 -Inf  Inf 0.2368851 0.01207915
checkresiduals(fit_AR5)

## 
##  Ljung-Box test
## 
## data:  Residuals from Regression with ARIMA(2,1,2) errors
## Q* = 218.32, df = 160, p-value = 0.001501
## 
## Model df: 4.   Total lags used: 164
#RMSE = 16059.29, MAE = 10298.89
fit5_AR <- sarima(turbine_tsi, 2, 1, 2,xreg = day_turbine1$wind_speed)
## initial  value 9.753309 
## iter   2 value 9.744518
## iter   3 value 9.739097
## iter   4 value 9.737658
## iter   5 value 9.732995
## iter   6 value 9.730230
## iter   7 value 9.726200
## iter   8 value 9.722472
## iter   9 value 9.704696
## iter  10 value 9.697101
## iter  11 value 9.692904
## iter  12 value 9.692020
## iter  13 value 9.688949
## iter  14 value 9.686856
## iter  15 value 9.686612
## iter  16 value 9.686320
## iter  17 value 9.686184
## iter  18 value 9.686072
## iter  19 value 9.686016
## iter  20 value 9.685989
## iter  21 value 9.685988
## iter  22 value 9.685983
## iter  23 value 9.685976
## iter  24 value 9.685940
## iter  25 value 9.685927
## iter  26 value 9.685918
## iter  27 value 9.685910
## iter  28 value 9.685898
## iter  29 value 9.685890
## iter  30 value 9.685888
## iter  30 value 9.685888
## iter  30 value 9.685888
## final  value 9.685888 
## converged
## initial  value 9.685431 
## iter   2 value 9.685422
## iter   3 value 9.685418
## iter   4 value 9.685417
## iter   5 value 9.685416
## iter   6 value 9.685416
## iter   7 value 9.685415
## iter   7 value 9.685415
## iter   7 value 9.685415
## final  value 9.685415 
## converged

fit5_AR
## $fit
## 
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, 
##     Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc, 
##     REPORT = 1, reltol = tol))
## 
## Coefficients:
##          ar1     ar2      ma1      ma2        xreg
##       0.3350  0.2391  -0.4383  -0.5143  27315.5935
## s.e.  0.2129  0.1734   0.2009   0.1979    589.4629
## 
## sigma^2 estimated as 258215749:  log likelihood = -9094.47,  aic = 18200.93
## 
## $degrees_of_freedom
## [1] 814
## 
## $ttable
##        Estimate       SE t.value p.value
## ar1      0.3350   0.2129  1.5731  0.1161
## ar2      0.2391   0.1734  1.3785  0.1684
## ma1     -0.4383   0.2009 -2.1819  0.0294
## ma2     -0.5143   0.1979 -2.5992  0.0095
## xreg 27315.5935 589.4629 46.3398  0.0000
## 
## $AIC
## [1] 22.22336
## 
## $AICc
## [1] 22.22345
## 
## $BIC
## [1] 22.25785
#Residuals are not white noise; ar1 and ar2 are not significant


fit_AR3 <- Arima(turbine_tsi, xreg = day_turbine1$wind_speed, order = c(2,1,1))
summary(fit_AR3)
## Series: turbine_tsi 
## Regression with ARIMA(2,1,1) errors 
## 
## Coefficients:
##          ar1      ar2      ma1        xreg
##       0.8637  -0.1753  -0.9621  27316.7580
## s.e.  0.0361   0.0355   0.0125    589.2288
## 
## sigma^2 = 259262026:  log likelihood = -9094.11
## AIC=18198.21   AICc=18198.29   BIC=18221.75
## 
## Training set error measures:
##                    ME     RMSE      MAE  MPE MAPE      MASE         ACF1
## Training set 95.09323 16052.45 10319.95 -Inf  Inf 0.2373695 -0.002897159
checkresiduals(fit_AR3)

## 
##  Ljung-Box test
## 
## data:  Residuals from Regression with ARIMA(2,1,1) errors
## Q* = 229.75, df = 161, p-value = 0.0003047
## 
## Model df: 3.   Total lags used: 164
#RMSE = 16052.45, MAE = 10319.95, final model
fit3_AR <- sarima(turbine_tsi, 2, 1, 1,xreg = day_turbine1$wind_speed)
## initial  value 9.753309 
## iter   2 value 9.743147
## iter   3 value 9.743025
## iter   4 value 9.742825
## iter   5 value 9.742674
## iter   6 value 9.741374
## iter   7 value 9.739876
## iter   8 value 9.738678
## iter   9 value 9.736465
## iter  10 value 9.731963
## iter  11 value 9.718832
## iter  12 value 9.697546
## iter  13 value 9.696918
## iter  14 value 9.695169
## iter  15 value 9.685697
## iter  16 value 9.684245
## iter  16 value 9.684245
## iter  17 value 9.683087
## iter  17 value 9.683087
## iter  18 value 9.683086
## iter  18 value 9.683086
## iter  18 value 9.683086
## final  value 9.683086 
## converged
## initial  value 9.689189 
## iter   2 value 9.686989
## iter   3 value 9.686621
## iter   4 value 9.685313
## iter   5 value 9.685113
## iter   6 value 9.685077
## iter   7 value 9.684987
## iter   8 value 9.684978
## iter   9 value 9.684977
## iter   9 value 9.684977
## iter   9 value 9.684977
## final  value 9.684977 
## converged

fit3_AR
## $fit
## 
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, 
##     Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc, 
##     REPORT = 1, reltol = tol))
## 
## Coefficients:
##          ar1      ar2      ma1        xreg
##       0.8637  -0.1753  -0.9621  27316.7580
## s.e.  0.0361   0.0355   0.0125    589.2288
## 
## sigma^2 estimated as 2.58e+08:  log likelihood = -9094.11,  aic = 18198.21
## 
## $degrees_of_freedom
## [1] 815
## 
## $ttable
##        Estimate       SE  t.value p.value
## ar1      0.8637   0.0361  23.8942       0
## ar2     -0.1753   0.0355  -4.9422       0
## ma1     -0.9621   0.0125 -76.8522       0
## xreg 27316.7580 589.2288  46.3602       0
## 
## $AIC
## [1] 22.22004
## 
## $AICc
## [1] 22.2201
## 
## $BIC
## [1] 22.24878
#All the terms are significant

day_turbine2 <- day_turbine1 %>%
  dplyr::select(ambient_temperature, wind_speed) 

day_turbine3 <- subset(day_turbine2, select = -c(year,month))


fit_AR6 <- Arima(turbine_tsi, xreg = as.matrix(day_turbine3), order = c(2,1,1))
summary(fit_AR6)
## Series: turbine_tsi 
## Regression with ARIMA(2,1,1) errors 
## 
## Coefficients:
##          ar1      ar2      ma1  ambient_temperature  wind_speed
##       0.8657  -0.1780  -0.9618            -741.0703  27282.4314
## s.e.  0.0360   0.0355   0.0118             395.0563    584.3959
## 
## sigma^2 = 258466379:  log likelihood = -9092.34
## AIC=18196.69   AICc=18196.79   BIC=18224.94
## 
## Training set error measures:
##                    ME     RMSE      MAE  MPE MAPE      MASE         ACF1
## Training set 122.1142 16017.96 10295.71 -Inf  Inf 0.2368121 -0.003687783
checkresiduals(fit_AR6)

## 
##  Ljung-Box test
## 
## data:  Residuals from Regression with ARIMA(2,1,1) errors
## Q* = 227.89, df = 161, p-value = 0.0004117
## 
## Model df: 3.   Total lags used: 164
fit_AR7 <- Arima(turbine_tsi, xreg = as.matrix(day_turbine3), order = c(1,0,1))
summary(fit_AR7)
## Series: turbine_tsi 
## Regression with ARIMA(1,0,1) errors 
## 
## Coefficients:
##          ar1     ma1  intercept  ambient_temperature  wind_speed
##       0.7049  0.2028  -62753.58            -452.6613  27905.0986
## s.e.  0.0340  0.0461   11644.31             374.5446    574.9022
## 
## sigma^2 = 259500585:  log likelihood = -9104.97
## AIC=18221.94   AICc=18222.04   BIC=18250.2
## 
## Training set error measures:
##                    ME     RMSE     MAE  MPE MAPE      MASE          ACF1
## Training set 9.267208 16059.83 10327.9 -Inf  Inf 0.2375523 -0.0005434625
checkresiduals(fit_AR7)

## 
##  Ljung-Box test
## 
## data:  Residuals from Regression with ARIMA(1,0,1) errors
## Q* = 256.31, df = 162, p-value = 3.299e-06
## 
## Model df: 2.   Total lags used: 164
#RMSE: 16059.83 MAE:10327.9

fit8_AR <- sarima(turbine_tsi, 2, 1, 1,xreg = as.matrix(day_turbine3))
## initial  value 9.751478 
## iter   2 value 9.741750
## iter   3 value 9.741607
## iter   4 value 9.741390
## iter   5 value 9.741237
## iter   6 value 9.740038
## iter   7 value 9.737884
## iter   8 value 9.731052
## iter   9 value 9.718287
## iter  10 value 9.707457
## iter  11 value 9.698241
## iter  12 value 9.690002
## iter  13 value 9.687652
## iter  14 value 9.685888
## iter  15 value 9.684702
## iter  16 value 9.684025
## iter  17 value 9.683474
## iter  18 value 9.683401
## iter  19 value 9.683394
## iter  20 value 9.683392
## iter  21 value 9.683392
## iter  22 value 9.683391
## iter  23 value 9.683389
## iter  24 value 9.683388
## iter  25 value 9.683388
## iter  25 value 9.683388
## iter  25 value 9.683388
## final  value 9.683388 
## converged
## initial  value 9.682834 
## iter   2 value 9.682827
## iter   3 value 9.682825
## iter   4 value 9.682825
## iter   4 value 9.682825
## iter   4 value 9.682825
## final  value 9.682825 
## converged

fit8_AR
## $fit
## 
## Call:
## stats::arima(x = xdata, order = c(p, d, q), seasonal = list(order = c(P, D, 
##     Q), period = S), xreg = xreg, transform.pars = trans, fixed = fixed, optim.control = list(trace = trc, 
##     REPORT = 1, reltol = tol))
## 
## Coefficients:
##          ar1      ar2      ma1  ambient_temperature  wind_speed
##       0.8657  -0.1780  -0.9618            -741.0703  27282.4314
## s.e.  0.0360   0.0355   0.0118             395.0563    584.3959
## 
## sigma^2 estimated as 256888436:  log likelihood = -9092.34,  aic = 18196.69
## 
## $degrees_of_freedom
## [1] 814
## 
## $ttable
##                       Estimate       SE  t.value p.value
## ar1                     0.8657   0.0360  24.0276   0.000
## ar2                    -0.1780   0.0355  -5.0221   0.000
## ma1                    -0.9618   0.0118 -81.4843   0.000
## ambient_temperature  -741.0703 395.0563  -1.8759   0.061
## wind_speed          27282.4314 584.3959  46.6848   0.000
## 
## $AIC
## [1] 22.21818
## 
## $AICc
## [1] 22.21827
## 
## $BIC
## [1] 22.25267
#RMSE = 16017.96, MAE = 10295.71, better than auto.arima, all the terms are significant, final model


accuracy(fit_AR3)
##                    ME     RMSE      MAE  MPE MAPE      MASE         ACF1
## Training set 95.09323 16052.45 10319.95 -Inf  Inf 0.2373695 -0.002897159
autoplot(forecast(fit_AR3, xreg = day_turbine1$wind_speed))

fit_AR3 %>% 
  forecast(xreg = day_turbine1$wind_speed, h=5)
##           Point Forecast       Lo 80     Hi 80        Lo 95     Hi 95
## 2020.2466     45078.3186  24443.2679  65713.37   13519.7319  76636.91
## 2020.2493     62630.4158  34846.9480  90413.88   20139.2686 105121.56
## 2020.2521     56065.4931  25291.5225  86839.46    9000.7665 103130.22
## 2020.2548     69129.7260  37080.6595 101178.79   20114.9085 118144.54
## 2020.2575     50686.7106  18044.8884  83328.53     765.3516 100608.07
## 2020.2603     33479.5874    520.6168  66438.56  -16926.8083  83885.98
## 2020.2630     73782.9851  40624.0776 106941.89   23070.8122 124495.16
## 2020.2658    113424.7101  80119.1099 146730.31   62488.1901 164361.23
## 2020.2685     83082.7729  49656.1979 116509.35   31961.2380 134204.31
## 2020.2712     75992.9393  42458.4278 109527.45   24706.3298 127279.55
## 2020.2740     72230.1099  38594.5200 105865.70   20788.9143 123671.31
## 2020.2767     35418.4035   1685.4592  69151.35  -16171.6828  87008.49
## 2020.2795     60814.5897  26986.3856  94642.79    9078.8162 112550.36
## 2020.2822     76466.7075  42544.4786 110388.94   24587.1353 128346.28
## 2020.2849     46887.6482  12872.1714  80903.12   -5134.5343  98909.83
## 2020.2877     70230.4718  36122.2790 104338.66   18066.4924 122394.45
## 2020.2904     65186.4556  30985.9465  99386.96   12881.2906 117491.62
## 2020.2932     80721.6537  46429.1563 115014.15   28275.8048 133167.50
## 2020.2959     63007.0623  28622.8655  97391.26   10420.9712 115593.15
## 2020.2986     49429.1149  14953.4853  83904.74   -3296.8105 102155.04
## 2020.3014     71319.4266  36752.6184 105886.23   18454.0555 124184.80
## 2020.3041     64439.1014  29781.3610  99096.84   11434.6615 117443.54
## 2020.3068      4177.3855 -30571.0456  38925.82  -48965.7538  57320.52
## 2020.3096     24182.0080 -10656.8758  59020.89  -29099.4668  77463.48
## 2020.3123     42460.4830   7531.3818  77389.58  -10958.9675  95879.93
## 2020.3151     42544.0229   7524.9372  77563.11  -11013.0470  96101.09
## 2020.3178     44225.9781   9117.1387  79334.82   -9468.3582  97920.31
## 2020.3205    101608.9034  66410.5395 136807.27   47777.6511 155440.16
## 2020.3233     93571.3039  58283.6426 128858.97   39603.4831 147539.12
## 2020.3260     87268.3168  51891.5836 122645.05   33164.2723 141372.36
## 2020.3288     80965.3298  45499.7485 116430.91   26725.4038 135205.26
## 2020.3315     74662.3429  39108.1354 110216.55   20286.8749 129037.81
## 2020.3342     68359.3560  32716.7428 104001.97   13848.6831 122870.03
## 2020.3370     62056.3691  26325.5689  97787.17    7410.8258 116701.91
## 2020.3397     55753.3822  19934.6121  91572.15     973.3005 110533.46
## 2020.3425     88489.2753  52582.7508 124395.80   33574.9849 143403.57
## 2020.3452     37800.8287   1806.7637  73794.89  -17247.3433  92849.00
## 2020.3479      7888.7030 -28192.6900  43970.10  -47293.0256  63070.43
## 2020.3507     -5503.1198 -41671.6300  30665.39  -60818.0827  49811.84
## 2020.3534     32225.1627  -4030.2554  68480.58  -23222.7144  87673.04
## 2020.3562     73456.0325  37113.9144 109798.15   17875.5592 129036.51
## 2020.3589    121857.7221  85429.1104 158286.33   66144.9682 177570.48
## 2020.3616     98562.0859  62047.1853 135076.99   42717.3646 154406.81
## 2020.3644    102733.7792  66132.7933 139334.77   46757.4017 158710.16
## 2020.3671    108996.2720  72309.4027 145683.14   52888.5472 165104.00
## 2020.3699     74140.1659  37367.6138 110912.72   17901.4006 130378.93
## 2020.3726     33631.1451  -3226.8907  70489.18  -22738.3562  90000.65
## 2020.3753     34296.6064  -2646.7151  71239.93  -22203.3282  90796.54
## 2020.3781     75540.4970  38512.0861 112568.91   18910.4294 132170.56
## 2020.3808     83496.2924  46382.9873 120609.60   26736.3903 140256.19
## 2020.3836     74627.4401  37429.4344 111825.45   17737.9996 131516.88
## 2020.3863     74834.5157  37552.0019 112117.03   17815.8312 131853.20
## 2020.3890     71174.9160  33808.0851 108541.75   14027.2798 128322.55
## 2020.3918     97407.9956  59957.0376 134858.95   40131.6980 154684.29
## 2020.3945     94208.7212  56673.8246 131743.62   36804.0505 151613.39
## 2020.3973     64571.4871  26952.8392 102190.14    7038.7299 122104.24
## 2020.4000     63029.3241  25327.1109 100731.54    5368.7648 120689.88
## 2020.4027     72563.2000  34777.6063 110348.79   14775.1213 130351.28
## 2020.4055     48919.9541  11051.1635  86788.74   -8995.3633 106835.27
## 2020.4082     72358.0517  34406.2467 110309.86   14315.7746 130400.33
## 2020.4110     78177.4859  40142.8476 116212.12   20008.5263 136346.45
## 2020.4137     83504.8764  45387.5848 121622.17   25209.5094 141800.24
## 2020.4164     85758.3260  47558.5599 123958.09   27336.8253 144179.83
## 2020.4192       690.5116 -37591.5512  38972.57  -57856.8512  59237.87
## 2020.4219     14333.8037 -24030.3795  52697.99  -44339.1513  73006.76
## 2020.4247     27977.0957 -10469.0323  66423.22  -30821.1831  86775.37
## 2020.4274     41620.3877   3092.4891  80148.29  -17302.9483 100543.72
## 2020.4301     55263.6797  16654.1838  93873.18   -3784.4487 114311.81
## 2020.4329     68906.9717  30216.0505 107597.89    9734.3141 128079.63
## 2020.4356     82550.2637  43778.0882 121322.44   23253.3384 141847.19
## 2020.4384     95192.0477  56338.7879 134045.31   35771.1146 154612.98
## 2020.4411     61967.5002  23033.3249 100901.68    2422.8175 121512.18
## 2020.4438     72504.8458  33489.9228 111519.77   12836.6702 132173.02
## 2020.4466     75151.2275  36055.7237 114246.73   15359.8140 134942.64
## 2020.4493     29512.3184  -9663.6006  68688.24  -30402.0794  89426.72
## 2020.4521     59236.8627  19980.6933  98493.03    -800.2676 119273.99
## 2020.4548     28921.2484 -10415.0078  68257.50  -31238.3639  89080.86
## 2020.4575     65525.1151  26108.9350 104941.30    5243.2696 125806.96
## 2020.4603     -6332.2879 -45828.2303  33163.65  -66736.1192  54071.54
## 2020.4630     13722.2848 -25853.2591  53297.83  -46803.2865  74247.86
## 2020.4658     38961.7748   -693.2108  78616.76  -21685.2921  99608.84
## 2020.4685     64201.2648  24466.9963 103935.53    3432.9452 124969.58
## 2020.4712     89440.7548  49627.3614 129254.15   28551.4240 150330.09
## 2020.4740    101837.8034  61945.4419 141730.16   40827.7013 162847.91
## 2020.4767     73546.9211  33575.7476 113518.09   12416.2864 134677.56
## 2020.4795     51163.6684  11113.8379  91213.50  -10087.2617 112414.60
## 2020.4822     56729.7509  16601.4176  96858.08   -4641.2388 118100.74
## 2020.4849     49821.3723   9614.6895  90028.06  -11669.4427 111312.19
## 2020.4877     79247.7288  38962.8489 119532.61   17637.3216 140858.14
## 2020.4904     42687.2922   2324.3666  83050.22  -19042.4755 104417.06
## 2020.4932     67910.0844  27469.2639 108350.90    6061.1866 129758.98
## 2020.4959     47455.0768   6936.5110  87973.64  -14512.7221 109422.88
## 2020.4986     40972.4950    376.3328  81568.66  -21113.9773 103058.97
## 2020.5014     58532.3989  17858.7884  99206.01   -3672.5204 120737.32
## 2020.5041     47739.4403   6988.5287  88490.35  -14583.7009 110062.58
## 2020.5068     45311.4093   4483.3429  86139.48  -17129.7299 107752.55
## 2020.5096     53815.9026  12910.8269  94720.98   -8743.0121 116374.82
## 2020.5123     65402.2667  24420.3265 106384.21    2725.7978 128078.74
## 2020.5151     44731.7796   3673.1187  85790.44  -18062.0235 107525.58
## 2020.5178     36072.3901  -5062.8483  77207.63  -26838.5282  98983.31
## 2020.5205     27413.0007 -13798.6730  68624.67  -35614.8153  90440.82
## 2020.5233     18753.6113 -22534.3562  60041.58  -44390.8859  81898.11
## 2020.5260     10094.2219 -31269.8987  51458.34  -53166.7414  73355.19
## 2020.5288      1434.8324 -40005.3012  42874.97  -61942.3828  64812.05
## 2020.5315     -7224.5570 -48740.5646  34291.45  -70717.8114  56268.70
## 2020.5342     47264.3041   5672.5611  88856.05  -16344.7777 110873.39
## 2020.5370     53204.3305  11536.9896  94871.67  -10520.3683 116929.03
## 2020.5397     40042.2572  -1700.5447  81785.06  -23797.8492 103882.36
## 2020.5425     45685.4156   3867.2889  87503.54  -18269.8902 109640.72
## 2020.5452     70711.9029  28818.5869 112605.22    6641.6050 134782.20
## 2020.5479     35305.1265  -6663.2441  77273.50  -28879.9575  99490.21
## 2020.5507     33780.2136  -8263.0777  75823.50  -30519.4517  98079.88
## 2020.5534     27057.1263 -15060.9524  69175.20  -37356.9164  91471.17
## 2020.5562     93393.8986  51201.1652 135586.63   28865.6812 157922.12
## 2020.5589     44140.0335   1872.7771  86407.29  -20502.1569 108782.22
## 2020.5616     53508.7734  11167.1251  95850.42  -11247.1895 118264.74
## 2020.5644     65119.4038  22703.4942 107535.31     249.8680 129988.94
## 2020.5671     52424.3148   9934.2737  94914.36  -12558.5954 117407.22
## 2020.5699     49879.7867   7315.7431  92443.83  -15216.3004 114975.87
## 2020.5726     69688.5536  27050.6361 112326.47    4479.4860 134897.62
## 2020.5753     83793.1183  41081.4545 126504.78   18471.2655 149114.97
## 2020.5781     65942.1938  23156.9110 108727.48     507.7504 131376.64
## 2020.5808    187714.0861 144855.3107 230572.86  122167.2454 253260.93
## 2020.5836    315933.2900 273001.1477 358865.43  250274.2444 381592.34
## 2020.5863    251525.6454 208520.2614 294531.03  185754.5863 317296.70
## 2020.5890    187118.0008 144039.4997 230196.50  121235.1187 253000.88
## 2020.5918    122710.3562  79558.8618 165861.85   56715.8405 188704.87
## 2020.5945     76722.0345  33497.6701 119946.40   10616.0738 142828.00
## 2020.5973     45960.7924   2663.6807  89257.90  -20256.4258 112178.01
## 2020.6000     51434.5393   8064.8023  94804.28  -14893.7497 117762.83
## 2020.6027     10169.3699 -33272.8711  53611.61  -56269.8043  76608.54
## 2020.6055     43652.2145    137.5904  87166.84  -22897.6601 110202.09
## 2020.6082    136001.5610  92414.6740 179588.45   69341.1698 202661.95
## 2020.6110    199841.8533 156182.8230 243500.88  133071.1284 266612.58
## 2020.6137    195160.4175 151429.3629 238891.47  128279.5410 262041.29
## 2020.6164    190478.9817 146676.0213 234281.94  123488.1347 257469.83
## 2020.6192    185797.5459 141922.7975 229672.29  118696.9086 252898.18
## 2020.6219    181116.1101 137169.6909 225062.53  113905.8618 248326.36
## 2020.6247    176434.6743 132416.7010 220452.65  109114.9936 243754.36
## 2020.6274    171753.2385 127663.8273 215842.65  104324.3029 239182.17
## 2020.6301     59258.0366  15097.3031 103418.77   -8279.9772 126796.05
## 2020.6329     30589.2588 -13642.6821  74821.20  -37057.6572  98236.17
## 2020.6356     32586.6638 -11716.3700  76889.70  -35168.9794 100342.31
## 2020.6384     42428.2626  -1945.7502  86802.28  -25435.9336 110292.46
## 2020.6411     47553.6406   3108.7621  91998.52  -20418.9353 115526.22
## 2020.6438     55625.1836  11109.5523 100140.81  -12455.5994 123705.97
## 2020.6466     42825.0612  -1761.2107  87411.33  -25363.7573 111013.88
## 2020.6493     30730.1543 -13926.6463  75386.95  -37566.5286  99026.84
## 2020.6521     93846.6542  49119.4359 138573.87   25442.2768 162251.03
## 2020.6548    104369.7490  59572.2238 149167.27   35857.8464 172881.65
## 2020.6575     63363.3428  18495.6208 108231.06   -5255.9164 131982.60
## 2020.6603     44584.5511   -353.2580  89522.36  -24141.8971 113311.00
## 2020.6630     73484.4441  28476.6571 118492.23    4650.9739 142317.91
## 2020.6658     95971.8656  50894.2093 141049.52   27031.5395 164912.19
## 2020.6685    105789.0068  60641.5893 150936.42   36741.9902 174836.02
## 2020.6712     77935.1382  32718.0672 123152.21    8781.5957 147088.68
## 2020.6740    127760.0385  82473.4211 173046.66   58500.1339 197019.94
## 2020.6767    123056.8096  77700.7523 168412.87   53690.7059 192422.91
## 2020.6795    155125.0832 109699.6923 200550.47   85652.9429 224597.22
## 2020.6822    207108.3905 161613.7716 252603.01  137530.3752 276686.41
## 2020.6849    214563.6459 168999.9042 260127.39  144879.9164 284247.38
## 2020.6877    233178.6758 187545.9160 278811.44  163389.3922 302967.96
## 2020.6904    250209.5955 204507.9219 295911.27  180314.9173 320104.27
## 2020.6932    160696.4940 114926.0103 206466.98   90696.5798 230696.41
## 2020.6959    142530.7465  96691.5560 188369.94   72425.7543 212635.74
## 2020.6986    109911.9018  64004.1073 155819.70   39701.9889 180121.81
## 2020.7014    159501.6523 113525.3562 205477.95   89186.9752 229816.33
## 2020.7041    191630.4052 145585.7094 237675.10  121211.1197 262049.69
## 2020.7068    170931.5174 124818.5233 217044.51  100407.7788 241455.26
## 2020.7096    166193.5398 120012.3485 212374.73   95565.5025 236821.58
## 2020.7123    161455.5622 115206.2742 207704.85   90723.3800 232187.74
## 2020.7151    156717.5845 110400.3000 203034.87   85881.4106 227553.76
## 2020.7178    151979.6069 105594.4255 198364.79   81039.5937 222919.62
## 2020.7205    147241.6293 100788.6503 193694.61   76197.9286 218285.33
## 2020.7233    142503.6517  95982.9738 189024.33   71356.4145 213650.89
## 2020.7260    187741.2694 141152.9910 234329.55  116490.6462 258991.89
## 2020.7288    229663.0578 183007.2769 276318.84  158309.1984 301016.92
## 2020.7315    165816.2784 119093.0926 212539.46   94359.3320 237273.22
## 2020.7342    115703.8503  68913.3565 162494.34   44143.9653 187263.74
## 2020.7370     92730.7535  45873.0485 139588.46   21068.0779 164393.43
## 2020.7397     81517.5490  34592.7291 128442.37    9752.2299 153282.87
## 2020.7425     73293.2525  26301.4135 120285.09    1425.4366 145161.07
## 2020.7452    129302.2632  82243.5006 176361.03   57332.0964 201272.43
## 2020.7479    136286.0400  89160.4487 183411.63   64213.6677 208358.41
## 2020.7507    171472.5858 124280.2606 218664.91   99298.1527 243647.02
## 2020.7534    197550.3209 150291.3560 244809.29  125273.9712 269826.67
## 2020.7562    191939.9439 144614.4331 239265.45  119561.8210 264318.07
## 2020.7589    174128.0215 126736.0582 221519.98  101648.2683 246607.77
## 2020.7616    153963.2878 106504.9651 201421.61   81382.0467 226544.53
## 2020.7644    178100.7242 130576.1348 225625.31  105418.1368 250783.31
## 2020.7671    198886.9864 151296.2225 246477.75  126103.1939 271670.78
## 2020.7699    215525.9779 167869.1314 263182.82  142641.1208 288410.83
## 2020.7726    199069.0869 151346.2494 246791.92  126083.3052 272054.87
## 2020.7753    199080.6769 151291.9394 246869.41  125994.1099 272167.24
## 2020.7781    245725.9469 197871.4001 293580.49  172538.7333 318913.16
## 2020.7808    270886.8447 222966.5792 318807.11  197599.1229 344174.57
## 2020.7836    274910.7298 226924.8355 322896.62  201522.6374 348298.82
## 2020.7863    240379.5239 192328.0903 288430.96  166891.1979 313867.85
## 2020.7890    219228.6807 171111.7973 267345.56  145640.2578 292817.10
## 2020.7918    233802.2010 185619.9565 281984.45  160113.8170 307490.58
## 2020.7945    234398.9697 186151.4528 282646.49  160610.7601 308187.18
## 2020.7973    222698.0738 174385.3726 271010.78  148810.1734 296585.97
## 2020.8000    214352.8735 165975.0758 262730.67  140365.4167 288340.33
## 2020.8027    181333.3795 132890.5729 229776.19  107246.5001 255420.26
## 2020.8055    180819.5642 132311.8357 229327.29  106633.3953 255005.73
## 2020.8082    180305.7489 131733.1853 228878.31  106020.4233 254591.07
## 2020.8110    179791.9335 131154.6213 228429.25  105407.5835 254176.28
## 2020.8137    179278.1182 130576.1434 227980.09  104794.8753 253761.36
## 2020.8164    178764.3029 129997.7513 227530.85  104182.2982 253346.31
## 2020.8192    178250.4876 129419.4445 227081.53  103569.8518 252931.12
## 2020.8219    172366.8052 123471.3557 221262.25   97587.6683 247145.94
## 2020.8247    195993.6137 147033.8426 244953.38  121116.1054 270871.12
## 2020.8274    200697.2677 151673.2593 249721.28  125721.5170 275673.02
## 2020.8301    200457.4096 151369.2481 249545.57  125383.5451 275531.27
## 2020.8329    137549.2329  88397.0019 186701.46   62377.3826 212721.08
## 2020.8356    191480.0892 142263.8722 240696.31  116210.3807 266749.80
## 2020.8384    212405.8292 163125.7092 261685.95  137038.3895 287773.27
## 2020.8411    212606.7105 163262.7703 261950.65  137141.6662 288071.75
## 2020.8438    208875.4381 159467.7601 258283.12  133312.9153 284437.96
## 2020.8466    131434.0079  81962.6743 180905.34   55774.1322 207093.88
## 2020.8493    163206.2673 113671.3598 212741.17   87449.1637 238963.37
## 2020.8521    206779.8719 157181.4721 256378.27  130925.6652 282634.08
## 2020.8548    211258.6337 161596.8227 260920.44  135307.4479 287209.82
## 2020.8575    251594.7128 201869.5714 301319.85  175546.6716 327642.75
## 2020.8603    191293.4962 141505.1051 241081.89  115148.7229 267438.27
## 2020.8630    145992.1055  96140.5448 195843.67   69750.7227 222233.49
## 2020.8658    191737.0671 141822.4168 241651.72  115399.1971 268074.94
## 2020.8685     41891.4091  -8086.2511  91869.07  -34542.8263 118325.64
## 2020.8712    225317.2124 175276.6216 275357.80  148786.7330 301847.69
## 2020.8740    300363.8640 250260.4216 350467.31  223737.2614 376990.47
## 2020.8767    302023.6891 251857.4739 352189.90  225301.0838 378746.29
## 2020.8795    236204.0190 185975.1095 286432.93  159385.5309 313022.51
## 2020.8822    224283.2288 173991.7030 274574.75  147368.9775 301197.48
## 2020.8849    192080.4352 141726.3711 242434.50  115070.5398 269090.33
## 2020.8877    190219.6377 139803.1129 240636.16  113114.2168 267325.06
## 2020.8904    154594.3443 104115.4360 205073.25   77393.5161 231795.17
## 2020.8932    166688.8130 116147.5982 217230.03   89392.6953 243984.93
## 2020.8959    172577.8065 121974.3620 223181.25   95186.5165 249969.10
## 2020.8986    175541.3930 124875.7951 226206.99   98055.0477 253027.74
## 2020.9014    172103.2344 121375.5593 222830.91   94521.9502 249684.52
## 2020.9041    151981.2969 101191.6205 202770.97   74305.1900 229657.40
## 2020.9068    142634.9101  91783.3080 193486.51   64864.0960 220405.72
## 2020.9096    159398.8728 108485.4203 210312.33   81533.4666 237264.28
## 2020.9123    135231.2052  84255.9774 186206.43   57271.3218 213191.09
## 2020.9151    139491.7495  88454.8211 190528.68   61437.5032 217546.00
## 2020.9178    123327.7796  72229.2252 174426.33   45179.2844 201476.27
## 2020.9205    121503.9204  70343.8141 172664.03   43261.2897 199746.55
## 2020.9233    142752.1906  91530.6064 193973.77   64415.5376 221088.84
## 2020.9260    168416.6828 117133.6944 219699.67   89986.1202 246847.25
## 2020.9288    172105.2626 120760.9435 223449.58   93580.9028 250629.62
## 2020.9315    115197.9315  63792.3548 166603.51   36579.8863 193815.98
## 2020.9342     41762.7855  -9703.9758  93229.55  -36948.8335 120474.40
## 2020.9370     25379.9440 -26147.9294  76907.82  -53425.1378 104185.03
## 2020.9397     44940.7356  -6648.1773  96529.65  -33957.6981 123839.17
## 2020.9425     24170.9573 -27478.9231  75820.84  -54820.7182 103162.63
## 2020.9452     57633.2133   5922.4373 109343.99  -21451.5939 136718.02
## 2020.9479     45351.5403  -6420.0597  97123.14  -33826.2892 124529.37
## 2020.9507     75569.0992  23736.7467 127401.45   -3701.6433 154839.84
## 2020.9534     74260.5085  22367.4745 126153.54   -5103.0383 153624.06
## 2020.9562     85460.4775  33506.8329 137414.12    6004.2347 164916.72
## 2020.9589     89882.1890  37868.0045 141896.37   10333.3584 169431.02
## 2020.9616     90001.4528  37926.7987 142076.11   10360.1420 169642.76
## 2020.9644     85696.4547  33561.4011 137831.51    5962.7709 165430.14
## 2020.9671     87887.8819  35692.4988 140083.27    8061.9320 167713.83
## 2020.9699     31276.4918 -20979.1513  83532.13  -48641.6177 111194.60
## 2020.9726     41702.0279 -10613.8057  94017.86  -38308.1350 121712.19
## 2020.9753     18159.0729 -34216.8820  70535.03  -61943.0377  98261.18
## 2020.9781     12878.2613 -39557.7459  65314.27  -67315.6914  93072.21
## 2020.9808     39728.1430 -12767.8480  92224.13  -40557.5469 120013.83
## 2020.9836     40894.9677 -11660.9385  93450.87  -39482.3546 121272.29
## 2020.9863     57907.6245   5291.8714 110523.38  -22561.2259 138376.47
## 2020.9890     43567.9637  -9107.5685  96243.50  -36992.3108 124128.24
## 2020.9918     58859.4498   6124.2064 111594.69  -21792.1451 139511.04
## 2020.9945     82292.3674  29497.4803 135087.25    1549.5552 163035.18
## 2020.9973     55100.8301   2246.3666 107955.29  -25733.0963 135934.76
## 2021.0000     30364.6599 -22549.3130  83278.63  -50560.2782 111289.60
## 2021.0027     54936.5397   1963.1244 107909.96  -26079.3077 135952.39
## 2021.0055     94256.1140  41223.3229 147288.91   13149.4590 175362.77
## 2021.0082     87003.0923  33910.9917 140095.19    5805.7314 168200.45
## 2021.0110     79377.4509  26226.1070 132528.79   -1910.5148 160665.42
## 2021.0137     48159.1930  -5051.3281 101369.71  -33219.2766 129537.66
## 2021.0164     31112.9502 -22156.6826  84382.58  -50355.9228 112581.82
## 2021.0192     70500.3055  17171.6267 123828.98  -11058.8706 152059.48
## 2021.0219     85807.4267  32419.7672 139195.09    4158.0474 167456.81
## 2021.0247     39973.9975 -13472.5776  93420.57  -41765.4855 121713.48
## 2021.0274     35058.4628 -18446.9632  88563.89  -46771.0247 116887.95
## 2021.0301     37696.5202 -15867.6919  91260.73  -44222.8729 119615.91
## 2021.0329     60433.1606   6810.2269 114056.09  -21576.0396 142442.36
## 2021.0356     44704.1496  -8977.4416  98385.74  -37394.7594 126803.06
## 2021.0384     34559.1616 -19181.0230  88299.35  -47629.3583 116747.68
## 2021.0411     17112.7999 -36685.9143  70911.51  -65165.2333  99390.83
## 2021.0438     42800.1987 -11056.9815  96657.38  -39567.2505 125167.65
## 2021.0466     50217.4755  -3698.1073 104133.06  -32239.2928 132674.24
## 2021.0493     86696.2478  32722.3257 140670.17    4150.2572 169242.24
## 2021.0521     41601.6588 -12430.5398  95633.86  -41033.4579 124236.78
## 2021.0548     72272.7610  18182.3488 126363.17  -10451.3858 154996.91
## 2021.0575     71840.2690  17691.7058 125988.83  -10972.8121 154653.35
## 2021.0603     79381.4352  25174.7833 133588.09   -3520.4848 162283.36
## 2021.0630     68638.1003  14373.4220 122902.78  -14352.5635 151628.76
## 2021.0658     60470.2419   6147.5991 114792.88  -22609.0710 143549.55
## 2021.0685     56867.2326   2486.6871 111247.78  -26300.6348 140035.10
## 2021.0712     55021.9985    583.6119 109460.39  -28234.3293 138278.33
## 2021.0740     44771.2984  -9724.8680  99267.46  -38573.3958 128115.99
## 2021.0767     84361.2512  29807.3663 138915.14     928.2841 167794.22
## 2021.0795     81475.2993  26863.7569 136086.84   -2045.8474 164996.45
## 2021.0822     72024.3531  17355.2139 126693.49  -11584.8802 155633.59
## 2021.0849     81535.4579  26808.7827 136262.13   -2161.7692 165232.69
## 2021.0877    118715.8723  63931.7213 173500.02   34930.7437 202501.00
## 2021.0904     80193.4877  25351.9214 135035.05   -3679.4502 164066.43
## 2021.0932     64219.2819   9320.3602 119118.20  -19741.3735 148179.94
## 2021.0959     96185.3553  41229.1380 151141.57   12137.0739 180233.64
## 2021.0986     78745.9041  23732.4509 133759.36   -5389.9120 162881.72
## 2021.1014     52655.6261  -2415.0034 107726.26  -31567.6337 136878.89
## 2021.1041     36907.9762 -18219.7704  92035.72  -47402.6366 121218.59
## 2021.1068     30920.3325 -24264.4720  86105.14  -53477.5429 115318.21
## 2021.1096     50916.3887  -4325.4149 106158.19  -33568.6592 135401.44
## 2021.1123     28151.2701 -27147.4737  83450.01  -56420.8604 112723.40
## 2021.1151     38167.5709 -17188.0546  93523.20  -46491.5526 122826.69
## 2021.1178     93492.7086  38080.2598 148905.16    8746.6813 178238.74
## 2021.1205     67393.8233  11924.6094 122863.04  -17439.0187 152226.67
## 2021.1233     69552.5887  14026.6677 125078.51  -15366.9793 154472.16
## 2021.1260     90925.5032  35342.9330 146508.07    5919.2977 175931.71
## 2021.1288    106423.8035  50784.6418 162062.97   21331.0488 191516.56
## 2021.1315     74978.1713  19282.4756 130673.87  -10201.0448 160157.39
## 2021.1342     67799.2266  12047.0541 123551.40  -17466.3632 153064.82
## 2021.1370     79760.0373  23951.4453 135568.63   -5591.8388 165111.91
## 2021.1397     82295.1987  26430.2441 138160.15   -3142.8765 167733.27
## 2021.1425    104500.8443  48579.5840 160422.10   18976.6569 190025.03
## 2021.1452     66672.1686  10694.6591 122649.68  -18938.0445 152282.38
## 2021.1479     69698.6685  13664.9664 125732.37  -15997.4838 155394.82
## 2021.1507     80773.9006  24684.0621 136863.74   -5008.1048 166555.91
## 2021.1534     63784.0994   7638.1807 119930.02  -22083.6733 149651.87
## 2021.1562     41776.6136 -14425.3294  97978.56  -44176.8409 127730.07
## 2021.1589     45293.9533 -10963.9582 101551.86  -40745.0976 131333.00
## 2021.1616     50949.9706  -5363.8537 107263.80  -35174.5917 137074.53
## 2021.1644     78424.3049  22054.6231 134793.99   -7785.6839 164634.29
## 2021.1671     79745.6135  23320.1296 136171.10   -6549.7173 166040.94
## 2021.1699     78333.9406  21852.7097 134815.17   -8046.6478 164714.53
## 2021.1726     66028.0308   9491.1079 122564.95  -20437.7312 152493.79
## 2021.1753     76953.0843  20360.5242 133545.64   -9597.7675 163503.94
## 2021.1781     74026.5032  17378.3605 130674.65  -12609.3548 160662.36
## 2021.1808     87300.8531  30597.1823 144004.52     580.0722 174021.63
## 2021.1836     84530.8166  27771.6721 141289.96   -2274.8040 171336.44
## 2021.1863     55607.4353  -1207.1288 112422.00  -31282.9423 142497.81
## 2021.1890     77715.8617  20845.9321 134585.79   -9259.1902 164690.91
## 2021.1918     65007.8775   8082.6361 121933.12  -22051.7665 152067.52
## 2021.1945     69356.2801  12375.7806 126336.78  -17787.8738 156500.43
## 2021.1973     84063.7528  27028.0489 141099.46   -3164.8290 171292.33
## 2021.2000    103072.3244  45981.4693 160163.18   15759.3962 190385.25
## 2021.2027     32167.1373 -24978.8157  89313.09  -55230.0559 119564.33
## 2021.2055     68878.2925  11677.2947 126079.29  -18603.0844 156359.67
## 2021.2082     53648.8087  -3607.1810 110904.80  -33916.6711 141214.29
## 2021.2110     42265.5770 -15045.3519  99576.51  -45383.9250 129915.08
## 2021.2137     79044.1030  21678.2876 136409.92   -8689.3407 166777.55
## 2021.2164     55062.5869  -2358.0626 112483.24  -32754.7183 142879.89
## 2021.2192     66701.6516   9226.2204 124177.08  -21199.4350 154602.74
## 2021.2219     99976.9670  42446.8062 157507.13   11992.1786 187961.76
## 2021.2247     73762.3326  16177.4942 131347.17  -14306.0778 161830.74
## 2021.2274     63789.5180   6150.0540 121428.98  -24362.4352 151941.47
## 2021.2301     62344.8008   4650.7627 120038.84  -25890.6162 150580.22
## 2021.2329     49179.1714  -8569.3891 106927.73  -39139.6304 137497.97
## 2021.2356     70826.4583  13023.4269 128629.49  -17575.6496 159228.57
## 2021.2384     87335.9551  29478.5040 145193.41   -1149.3806 175821.29
## 2021.2411     71099.5370  13187.7173 129011.36  -17468.9482 159668.02
## 2021.2438     56935.8155  -1030.3218 114901.95  -31715.7413 145587.37
## 2021.2466     80446.9168  22426.5129 138467.32   -8287.6337 169181.47
## 2021.2493     79717.5259  21642.9059 137792.15   -9099.9409 168534.99
## 2021.2521     67579.3613   9450.5759 125708.15  -21320.9444 156479.67
## 2021.2548     90951.8198  32768.9193 149134.72    1968.7523 179934.89
## 2021.2575     88607.8305  30370.8653 146844.80    -457.9218 177673.58
## 2021.2603     97227.7005  38936.7208 155518.68    8079.3401 186376.06
## 2021.2630     71308.9528  12964.0085 129653.90  -17921.9394 160539.84
## 2021.2658     50774.4499  -7624.4091 109173.31  -38538.8977 140087.80
## 2021.2685     74899.4117  16446.6876 133352.14  -14496.3153 164295.14
## 2021.2712    103302.2398  44795.7003 161808.78   13824.2092 192780.27
## 2021.2740     80221.5155  21661.2102 138781.82   -9338.7429 169781.77
## 2021.2767    102445.1597  43831.1378 161059.18   12802.7488 192087.57
## 2021.2795     92564.5410  33896.8516 151232.23    2840.0528 182289.03
## 2021.2822     92790.8672  34069.5594 151512.18    2984.3768 182597.36
## 2021.2849     68135.2390   9360.3618 126910.12  -21753.1788 158023.66
## 2021.2877     63812.2007   4983.8027 122640.60  -26158.0700 153782.47
## 2021.2904     81203.3985  22321.5285 140085.27   -8848.6506 171255.45
## 2021.2932     64235.6688   5300.3753 123170.96  -25898.0845 154369.42
## 2021.2959     54832.3663  -4156.3023 113821.03  -35383.0173 145047.75
## 2021.2986     67852.2154   8810.2198 126894.21  -22444.7246 158149.16
## 2021.3014     94854.3363  35759.0620 153949.61    4475.9134 185232.76
## 2021.3041     70424.8486  11276.3435 129573.35  -20034.9838 160884.68
## 2021.3068     55819.0273  -3382.6607 115020.72  -34722.1413 146360.20
## 2021.3096     65356.5010   6101.6778 124611.32  -25265.9308 155978.93
## 2021.3123     92675.5291  33367.6183 151983.44    1971.9068 183379.15
## 2021.3151    157191.1885  97830.2376 216552.14   66406.4484 247975.93
## 2021.3178    119654.8776  60240.9339 179068.82   28789.0920 210520.66
## 2021.3205     65166.0426   5699.1535 124632.93  -25780.7161 156112.80
## 2021.3233     50333.5157  -9186.2719 109853.30  -40694.1442 141361.18
## 2021.3260     73443.3860  13870.7470 133016.03  -17665.1032 164551.88
## 2021.3288    108168.2599  48542.8163 167793.70   16979.0130 199357.51
## 2021.3315     70526.9986  10848.7971 130205.20  -20742.9345 161796.93
## 2021.3342     60510.5206    779.6078 120241.43  -30840.0274 151861.07
## 2021.3370     90426.8555  30643.2778 150210.43   -1004.2365 181857.95
## 2021.3397    107745.2110  47909.0149 167581.41   16233.6460 199256.78
## 2021.3425     95031.9909  35143.2226 154920.76    3440.0237 186623.96
## 2021.3452     81765.4952  21824.2007 141706.79   -9906.8038 173437.79
## 2021.3479     66432.5872   6438.8127 126426.36  -25319.9732 158185.15
## 2021.3507     58048.5187  -1997.6901 118094.73  -33784.2330 149881.27
## 2021.3534     75280.1488  15181.5514 135378.75  -16632.7243 167193.02
## 2021.3562    110537.4646  50386.5244 170688.40   18544.5400 202530.39
## 2021.3589    136048.6299  75845.3923 196251.87   43975.7234 228121.54
## 2021.3616    113640.2934  53384.8037 173895.78   21487.4743 205793.11
## 2021.3644     86886.7687  26579.0724 147194.47   -5345.8936 179119.43
## 2021.3671    104436.0641  44076.2062 164795.92   12123.6276 196748.50
## 2021.3699     48578.6790 -11833.2955 108990.65  -43813.4630 140970.82
## 2021.3726     37331.6134 -23132.4327  97795.66  -55140.1652 129803.39
## 2021.3753     25876.0748 -34639.9981  86392.15  -66675.2719 118427.42
## 2021.3781     44645.6289 -15922.4261 105213.68  -47985.2176 137276.48
## 2021.3808     93115.3642  32495.3717 153735.36     405.0861 185825.64
## 2021.3836    107956.4507  47284.5652 168628.34   15166.8090 200746.09
## 2021.3863     92858.6696  32134.9353 153582.40     -10.2679 185727.61
## 2021.3890     87231.7407  26456.2019 148007.28   -5716.4249 180179.91
## 2021.3918     78317.4308  17490.1317 139144.73  -14709.8954 171344.76
## 2021.3945     84262.5360  23383.5205 145141.55   -8843.8836 177368.96
## 2021.3973     51832.5489  -9098.1391 112763.24  -41352.8970 145017.99
## 2021.4000     45452.3056 -15530.0111 106434.62  -47812.0995 138716.71
## 2021.4027     25391.5617 -35642.3400  86425.46  -67951.7359 118734.86
## 2021.4055     62020.3581    934.9149 123105.80  -31401.7653 155442.48
## 2021.4082     76925.2724  15788.3313 138062.21  -16575.6104 170426.16
## 2021.4110    115231.6438  54043.2480 176420.04   21652.0678 208811.22
## 2021.4137     39552.6591 -21687.1482 100792.47  -54105.5439 133210.86
## 2021.4164     44595.1801 -16695.9955 105886.36  -49141.5839 138331.94
## 2021.4192     47541.7582 -13800.7426 108884.26  -46273.5010 141357.02
## 2021.4219     71223.5844   9829.8012 132617.37  -22670.1044 165117.27
## 2021.4247     64456.3388   3011.3160 125901.36  -29515.7142 158428.39
## 2021.4274     64160.0879   2663.8682 125656.31  -29890.2640 158210.44
## 2021.4301     53716.9249  -7830.4490 115264.30  -40411.6607 147845.51
## 2021.4329     44199.5583 -17398.9275 105798.04  -50007.1962 138406.31
## 2021.4356     57026.9972  -4622.5580 118676.55  -37257.8612 151311.86
## 2021.4384     63616.1753   1915.5929 125316.76  -30746.7224 157979.07
## 2021.4411     65412.5104   3660.9430 127164.08  -29028.3622 159853.38
## 2021.4438     90540.7507  28738.2404 152343.26   -3978.0323 185059.53
## 2021.4466     98127.9354  36274.5241 159981.35    3531.3060 192724.56
## 2021.4493    123163.0825  61258.8120 185067.35   28488.6707 217837.49
## 2021.4521     87826.7186  25871.6307 149781.81   -6925.4117 182578.85
## 2021.4548     89580.9064  27575.0429 151586.77   -5248.8786 184410.69
## 2021.4575     52044.8452 -10011.7526 114101.44  -42862.5311 146952.22
## 2021.4603     78135.5145  16028.2240 140242.81  -16849.3896 173120.42
## 2021.4630     69025.3437   6867.4018 131183.29  -26037.0250 164087.71
## 2021.4658     60303.4043  -1905.1478 122511.96  -34836.3660 155443.17
## 2021.4685     48575.6295 -13683.4916 110834.75  -46641.4795 143792.74
## 2021.4712     59607.2034  -2702.4457 121916.85  -35687.1815 154901.59
## 2021.4740     65929.0659   3568.9298 128289.20  -29442.5322 161300.66
## 2021.4767     73335.2702  10924.6879 135745.85  -22113.4787 168784.02
## 2021.4795     70168.6594   7707.6717 132629.65  -25357.1780 165694.50
## 2021.4822     47041.5574 -15469.7952 109552.91  -48561.3064 142644.42
## 2021.4849     38910.3350 -23651.3419 101472.01  -56769.4931 134590.16
## 2021.4877     77290.7248  14678.7641 139902.69  -18466.0057 173047.46
## 2021.4904     68000.8350   5338.6309 130663.04  -27832.7362 163834.41
## 2021.4932     39932.0231 -22780.3843 102644.43  -55978.3274 135842.37
## 2021.4959     35162.9599 -27599.6105  97925.53  -60824.1083 131150.03
## 2021.4986     65566.3927   2753.6993 128379.09  -30497.3320 161630.12
## 2021.5014     54115.7237  -8747.0528 116978.50  -42024.5965 150256.04
## 2021.5041     39336.8472 -23575.9723 102249.67  -56880.0073 135553.70
## 2021.5068     52136.2340 -10826.5890 115099.06  -44157.0941 148429.56
## 2021.5096     70995.9923   7983.2056 134008.78  -25373.7487 167365.73
## 2021.5123     46894.7381 -16167.9727 109957.45  -49551.3552 143340.83
## 2021.5151     53160.1408  -9952.4547 116272.74  -43362.2446 149682.53
## 2021.5178     47227.5736 -15934.8671 110390.01  -49371.0434 143826.19
## 2021.5205     50455.2831 -12756.9635 113667.53  -46219.5055 147130.07
## 2021.5233     55398.9851  -7863.0282 118661.00  -41351.9151 152149.89
## 2021.5260     42671.7467 -20639.9942 105983.49  -54155.2053 139498.70
## 2021.5288     58561.3746  -4800.0548 121922.80  -38341.5695 155464.32
## 2021.5315     63305.9070   -105.1721 126716.99  -33672.9697 160284.78
## 2021.5342     58078.9582  -5381.7317 121539.65  -38975.7917 155133.71
## 2021.5370     45749.7627 -17760.4992 109260.02  -51380.8010 142880.33
## 2021.5397     48550.3577 -15009.4376 112110.15  -48655.9608 145756.68
## 2021.5425     54835.2725  -8774.0176 118444.56  -42446.7418 152117.29
## 2021.5452     60526.8919  -3131.8545 124185.64  -36830.7593 157884.54
## 2021.5479     35443.2241 -28264.9403  99151.39  -61990.0053 132876.45
## 2021.5507     43331.3477 -20426.1963 107088.89  -54177.4013 140840.10
## 2021.5534     49998.3300 -13808.5554 113805.22  -47585.8802 147582.54
## 2021.5562     69294.0384   5437.8498 133150.23  -28365.5746 166953.65
## 2021.5589     71203.4146   7297.9607 135108.87  -26531.5431 168938.37
## 2021.5616     45079.2811 -18875.4001 109033.96  -52730.9633 142889.53
## 2021.5644     74569.3850  10565.5144 138573.26  -23316.0881 172454.86
## 2021.5671     46811.2550 -17241.7672 110864.28  -51149.3890 144771.90
## 2021.5699     33193.4501 -30908.6861  97295.59  -64842.3072 131229.21
## 2021.5726    104260.6110  40109.3984 168411.82    6149.7978 202371.42
## 2021.5753    119237.1399  55036.8885 183437.39   21051.3282 217422.95
## 2021.5781    177544.2813 113295.0284 241793.53   79283.5284 275805.03
## 2021.5808    131460.6229  67162.4060 195758.84   33124.9860 229796.26
## 2021.5836     84062.8375  19715.6937 148409.98  -14347.6266 182473.30
## 2021.5863     61164.3378  -3231.6957 125560.37  -37320.8966 159649.57
## 2021.5890     67408.3827   2963.4967 131853.27  -31151.5652 165968.33
## 2021.5918    129321.7444  64828.0428 193815.45   30687.1395 227956.35
## 2021.5945    138400.4733  73857.9932 202942.95   39691.2680 237109.68
## 2021.5973    115283.5979  50692.3759 179874.82   16499.8484 214067.35
## 2021.6000     54741.5667  -9898.3603 119381.49  -44116.6707 153599.80
## 2021.6027     69176.4427   4487.8473 133865.04  -29756.2265 168109.11
## 2021.6055     49375.6151 -15361.6121 114112.84  -49631.4301 148382.66
## 2021.6082     77969.5246  13183.7022 142755.35  -21111.8406 177050.89
## 2021.6110     60276.2015  -4558.1798 125110.58  -38879.4281 159431.83
## 2021.6137     78084.5495  13201.6457 142967.45  -21145.2888 177314.39
## 2021.6164     35084.1046 -29847.2854 100015.49  -64219.8870 134388.10
## 2021.6192     50944.6589 -14035.1812 115924.50  -48433.4307 150322.75
## 2021.6219     46003.3358 -19024.9183 111031.59  -53448.7966 145455.47
## 2021.6247     43525.0171 -21551.6150 108601.65  -56001.1030 143051.14
## 2021.6274     26850.4218 -38274.5522  91975.40  -72749.6310 126450.47
## 2021.6301     54104.4845 -11068.7957 119277.76  -45569.4462 153778.42
## 2021.6329     37089.3075 -28132.2431 102310.86  -62658.4464 136837.06
## 2021.6356     54708.3199 -10561.4654 119978.11  -45113.2026 154529.84
## 2021.6384     51710.4413 -13607.5431 117028.43  -48184.7953 151605.68
## 2021.6411     72287.3849   6921.2370 137653.53  -27681.5115 172256.28
## 2021.6438     50861.8686 -14552.4074 116276.14  -49180.6333 150904.37
## 2021.6466    -13364.5089 -78826.8775  52097.86 -113480.5622  86751.54
## 2021.6493     12750.5652 -52759.8608  78260.99  -87438.9855 112940.12
## 2021.6521     40913.6571 -24644.7911 106472.11  -59349.3372 141176.65
## 2021.6548     47976.2952 -17630.1400 113582.73  -52360.0888 148312.68
## 2021.6575     91833.0260  26178.6389 157487.41   -8576.6942 192242.75
## 2021.6603     70198.7826   4496.4786 135901.09  -30284.2202 170681.79
## 2021.6630    119165.9106  53415.7246 184916.10   18609.6786 219722.14
## 2021.6658     99441.0283  33642.9952 165239.06   -1188.3795 200070.44
## 2021.6685     88061.9719  22216.1264 153907.82  -12640.5587 188764.50
## 2021.6712     66191.7568    298.1336 132085.38  -34583.8435 166967.36
## 2021.6740     49286.6318 -16654.7345 115228.00  -51561.9852 150135.25
## 2021.6767     54286.7697 -11702.3051 120275.84  -46634.8112 155208.35
## 2021.6795     38277.7916 -27758.9573 104314.54  -62716.7006 139272.28
## 2021.6822     95336.3916  29252.0030 161420.78   -5730.9592 196403.74
## 2021.6849     50170.0890 -15961.9049 116302.08  -50970.0678 151310.25
## 2021.6877     74821.3611   8641.7961 141000.93  -26391.5495 176034.27
## 2021.6904    144956.0403  78728.9383 211183.14   43670.4282 246241.65
## 2021.6932    124146.2143  57871.6095 190420.82   22787.9529 225504.48
## 2021.6959    162120.9995  95798.9258 228443.07   60690.1407 263551.86
## 2021.6986    172961.0174 106591.5088 239330.53   71457.6133 274464.42
## 2021.7014    147878.0281  81461.1186 214294.94   46302.1305 249453.93
## 2021.7041    160038.2406  93573.9638 226502.52   58389.9010 261686.58
## 2021.7068    148081.5397  81569.9295 214593.15   46360.8098 249802.27
## 2021.7096    157293.8679  90734.9579 223852.78   55500.7993 259086.94
## 2021.7123    168766.1797 102160.0035 235372.36   66900.8237 270631.54
## 2021.7151    127343.1602  60689.7513 193996.57   25405.5680 229280.75
## 2021.7178     91906.8838  25206.2757 158607.49  -10102.8934 193916.66
## 2021.7205     84561.7349  17813.9609 151309.51  -17520.1763 186643.65
## 2021.7233     90540.2510  23745.3444 157335.16  -11613.7432 192694.25
## 2021.7260    112752.6110  45910.6051 179594.62   10526.5846 214978.64
## 2021.7288    171615.2908 104726.2187 238504.36   69317.2829 273913.30
## 2021.7315    204991.5228 138055.4177 271927.63  102621.5841 307361.46
## 2021.7342    232205.8221 165222.7170 299188.93  129764.0030 334647.64
## 2021.7370    217955.7950 150925.7227 284985.87  115442.1459 320469.44
## 2021.7397    224272.0892 157195.0828 291349.10  121686.6605 326857.52
## 2021.7425    198228.5522 131104.6444 265352.46   95571.3940 300885.71
## 2021.7452    219493.7497 152322.9733 286664.53  116764.9121 322222.59
## 2021.7479    206203.8208 138986.2084 273421.43  103403.3538 309004.29
## 2021.7507    211997.2236 144732.8079 279261.64  109125.1771 314869.27
## 2021.7534    203830.8614 136519.6749 271142.05  100887.2851 306774.44
## 2021.7562    203179.9682 135822.0433 270537.89  100164.9118 306195.02
## 2021.7589    202681.1543 135276.5235 270085.79   99594.6674 305767.64
## 2021.7616    205896.5772 138445.2729 273347.88  102738.7092 309054.45
## 2021.7644    201276.2600 133778.3144 268774.21   98047.0603 304505.46
## 2021.7671    209338.8747 141794.3200 276883.43  106038.3926 312639.36
## 2021.7699    207917.1904 140326.0587 275508.32  104545.4749 311288.91
## 2021.7726    126005.3999  58367.7233 193643.08   22562.5002 229448.30
## 2021.7753    116724.1475  49039.9580 184408.34   13210.1125 220238.18
## 2021.7781    133840.8740  66110.2036 201571.54   30255.7525 237426.00
## 2021.7808    133363.0564  65585.9369 201140.18   29706.8972 237019.22
## 2021.7836    117181.8962  49358.3596 185005.43   13454.7480 220909.04
## 2021.7863    112330.9197  44460.9975 180200.84    8532.8310 216129.01
## 2021.7890    111436.7584  43520.4824 179353.03    7567.7776 215305.74
## 2021.7918     87744.7668  19782.1686 155707.37  -16195.0576 191684.59
## 2021.7945     60888.1878  -7120.7010 128897.08  -43122.4321 164898.81
## 2021.7973     40103.7348 -27951.4132 108158.88  -63977.6323 144185.10
## 2021.8000     81380.1967  13278.8210 149481.57  -22771.8697 185532.26
## 2021.8027    142786.7684  74639.1963 210934.34   38564.0507 247009.49
## 2021.8055    148566.9822  80373.2450 216760.72   44273.6611 252860.30
## 2021.8082    174512.9955 106273.1244 242752.87   70149.1188 278876.87
## 2021.8110    186283.5644 117997.5906 254569.54   81849.1797 290717.95
## 2021.8137    236533.8775 168201.8322 304865.92  132029.0324 341038.72
## 2021.8164    215385.4564 147007.3706 283763.54  110810.1984 319960.71
## 2021.8192    203138.0117 134713.9163 271562.11   98492.3881 307783.64
## 2021.8219    193658.1893 125188.1152 262128.26   88942.2475 298374.13
## 2021.8247    190616.2335 122100.2117 259132.26   85830.0206 295402.45
## 2021.8274    215355.4034 146793.4645 283917.34  110498.9665 320211.84
## 2021.8301    173833.7458 105225.9206 242441.57   68907.1319 278760.36
## 2021.8329    215428.7321 146775.0513 284082.41  110431.9881 320425.48
## 2021.8356    239938.1839 171238.6782 308637.69  134871.3567 345005.01
## 2021.8384    304656.1298 235910.8297 373401.43  199519.2660 409792.99
## 2021.8411    332223.7335 263432.6694 401014.80  227016.8798 437430.59
## 2021.8438    286137.3332 217300.5356 354974.13  180860.5360 391414.13
## 2021.8466    256944.4726 188061.9717 325826.97  151597.7784 362291.17
## 2021.8493    205261.3097 136333.1360 274189.48   99844.7649 310677.85
## 2021.8521    217500.8848 148527.0685 286474.70  112014.5357 322987.23
## 2021.8548    217447.2047 148427.7760 286466.63  111891.0974 323003.31
## 2021.8575    183797.5058 114732.4947 252862.52   78171.6863 289423.33
## 2021.8603    175366.9427 106256.3793 244477.51   69671.4571 281062.43
## 2021.8630    162550.0952  93394.0097 231706.18   56784.9894 268315.20
## 2021.8658    167031.6718  97830.0940 236233.25   61196.9915 272866.35
## 2021.8685    125012.5469  55765.5066 194259.59   19108.3378 230916.76
## 2021.8712    105042.8653  35750.3925 174335.34    -930.8269 211016.56
## 2021.8740     84909.1654  15571.2897 154247.04  -21133.9645 190952.30
## 2021.8767     77100.9018   7717.6530 146484.15  -29011.6202 183213.42
## 2021.8795     99913.0666  30484.4743 169341.66   -6268.8023 206094.94
## 2021.8822    107538.3809  38064.4748 177012.29    1287.2104 213789.55
## 2021.8849     94100.0431  24580.8527 163619.23  -12220.3837 200420.47
## 2021.8877    160417.0205  90852.5753 229981.47   54027.3824 266806.66
## 2021.8904    155331.2322  85721.5615 224940.90   48872.4278 261790.04
## 2021.8932    162142.1713  92487.3045 231797.04   55614.2454 268670.10
## 2021.8959    128848.9822  59148.9487 198549.02   22251.9797 235445.98
## 2021.8986    140650.7432  70905.5722 210395.91   33984.7089 247316.78
## 2021.9014     87518.7345  17728.4552 157309.01  -19216.2870 194253.76
## 2021.9041    133659.0367  63823.6782 203494.40   26855.0726 240463.00
## 2021.9068    196207.0984 126326.6898 266087.51   89334.2361 303079.96
## 2021.9096    167588.1831  97662.7535 237513.61   60646.4670 274529.90
## 2021.9123    109162.4243  39192.0025 179132.85    2151.8987 216172.95
## 2021.9151    185016.8207 115001.4358 255032.21   77937.5298 292096.11
## 2021.9178    198670.1132 128609.7939 268730.43   91522.1012 305818.13
## 2021.9205    211400.9739 141295.7491 281506.20  104184.2848 318617.66
## 2021.9233    237095.4852 166945.3836 307245.59  129810.1630 344380.81
## 2021.9260    236157.9670 165963.0173 306352.92  128804.0555 343511.88
## 2021.9288    199921.9254 129682.1562 270161.69   92499.4685 307344.38
## 2021.9315    203533.8898 133249.3298 273818.45   96042.9311 311024.85
## 2021.9342    213899.8088 143570.4864 284229.13  106340.3920 321459.23
## 2021.9370    150202.5781  79828.5218 220576.63   42574.7468 257830.41
## 2021.9397    142997.4243  72578.6626 213416.19   35301.2219 250693.63
## 2021.9425    163692.8027  93229.3639 234156.24   55928.2726 271457.33
## 2021.9452    156853.3490  86345.2614 227361.44   49020.5344 264686.16
## 2021.9479     92718.6973  22165.9891 163271.41  -15182.3585 200619.75
## 2021.9507    122071.2869  51473.9864 192668.59   14102.0330 230040.54
## 2021.9534     80400.5143   9758.6496 151042.38  -27636.8947 188437.92
## 2021.9562     71553.5454    867.1446 142239.95  -36551.9757 179659.07
## 2021.9589     67716.7128  -3014.1961 138447.62  -40456.8775 175890.30
## 2021.9616     22203.3491 -48572.0398  92978.74  -86038.2675 130444.97
## 2021.9644     40714.7966 -30105.0444 111534.64  -67594.8037 149024.40
## 2021.9671     35774.5517 -35089.7136 106638.82  -72602.9896 144152.09
## 2021.9699      2312.5890 -68596.0727  73221.25 -106132.8507 110758.03
## 2021.9726     32318.1541 -38634.8762 103271.18  -76195.1416 140831.45
## 2021.9753     39305.9455 -31691.4256 110303.32  -69275.1637 147887.05
## 2021.9781     47414.9043 -23626.7801 118456.59  -61233.9762 156063.78
## 2021.9808     22580.4431 -48505.5269  93666.41  -86136.1664 131297.05
## 2021.9836      8224.7185 -62905.5095  79354.95 -100559.5777 117009.01
## 2021.9863     29293.2245 -41881.2340 100467.68  -79558.7164 138145.17
## 2021.9890     42155.0928 -29063.5688 113373.75  -66764.4509 151074.64
## 2021.9918     42470.1754 -28792.6618 113733.01  -66516.9290 151457.28
## 2021.9945     28429.7920 -42877.1935  99736.78  -80624.8314 137484.42
## 2021.9973     29556.6467 -41794.4597 100907.75  -79565.4538 138678.75
## 2022.0000     16547.0406 -54848.1595  87942.24  -92642.4954 125736.58
## 2022.0027     17081.9929 -54357.2736  88521.26  -92174.9369 126338.92
## 2022.0055     16122.7923 -55360.5135  87606.10  -93201.4898 125447.07
## 2022.0082     24155.6144 -47371.7036  95682.93  -85235.9785 133547.21
## 2022.0110     24419.5048 -47151.7983  95990.81  -85039.3575 133878.37
## 2022.0137     10981.8293 -60633.4318  82597.09  -98544.2611 120507.92
## 2022.0164     20568.0245 -51091.1678  92227.22  -89025.2528 130161.30
## 2022.0192     12783.1981 -58919.8984  84486.29  -96877.2248 122443.62
## 2022.0219     13425.6011 -58321.3728  85172.57  -96301.9265 123153.13
## 2022.0247     31383.3622 -40407.4622 103174.19  -78411.2290 141177.95
## 2022.0274     42268.0908 -29566.5573 114102.74  -67593.5230 152129.70
## 2022.0301     45490.3317 -26388.1135 117368.78  -64438.2639 155418.93
## 2022.0329     56793.1483 -15129.0672 128715.36  -53202.3883 166788.68
## 2022.0356    112259.0155  40293.0561 184224.97    2196.5785 222321.45
## 2022.0384    107282.6492  35272.9727 179292.33   -2846.6474 217411.95
## 2022.0411     96352.3323  24298.9652 168405.70  -13843.7833 206548.45
## 2022.0438     85422.0155  13324.9842 157519.05  -24840.8788 195684.91
## 2022.0466     74491.6987   2351.0296 146632.37  -35837.9338 184821.33
## 2022.0493     45259.4856 -26924.7949 117443.77  -65136.8447 155655.82
## 2022.0521      8953.4189 -63274.4466  81181.28 -101509.5690 119416.41
## 2022.0548     57778.1014 -14493.3228 130049.53  -52751.5038 168307.71
## 2022.0575     37525.1881 -34789.7686 109840.14  -73070.9943 148121.37
## 2022.0603     33850.9013 -38507.5618 106209.36  -76811.8183 144513.62
## 2022.0630     56360.1118 -16041.8314 128762.06  -54369.1050 167089.33
## 2022.0658     31260.4587 -41184.9386 103705.86  -79535.2153 142056.13
## 2022.0685     62505.0205  -9983.8048 134993.85  -48357.0710 173367.11
## 2022.0712     55268.0192 -17264.2082 127800.25  -55660.4500 166196.49
## 2022.0740     96852.4872  24276.8838 169428.09  -14142.3200 207847.29
## 2022.0767     88647.1062  16028.1525 161266.06  -22413.9994 199708.21
## 2022.0795     68713.7546  -3948.5233 141376.03  -42413.6098 179841.12
## 2022.0822     48817.1677 -23888.4087 121522.74  -62376.4160 160010.75
## 2022.0849     48042.0719 -24706.7773 120790.92  -63217.6917 159301.84
## 2022.0877      2082.5295 -70709.5666  74874.63 -109243.3747 113408.43
## 2022.0904     11310.2904 -61525.0271  84145.61 -100081.7151 122702.30
## 2022.0932     12551.2690 -60327.2441  85429.78  -98906.7985 124009.34
## 2022.0959      9986.6594 -62935.0238  82908.34 -101537.4311 121510.75
## 2022.0986      5125.7285 -67839.0993  78090.56 -106464.3459 116715.80
## 2022.1014     17731.6770 -55276.2698  90739.62  -93924.3423 129387.70
## 2022.1041     43003.3429 -30047.6976 116054.38  -68718.5825 154725.27
## 2022.1068     59632.8178 -13461.2909 132726.93  -52154.9747 171420.61
## 2022.1096     59752.4648 -13384.6867 132889.62  -52101.1560 171606.09
## 2022.1123     53992.6122 -19187.5568 127172.78  -57926.7982 165912.02
## 2022.1151     31223.3374 -41999.8239 104446.50  -80761.8240 143208.50
## 2022.1178     43968.7185 -29297.4098 117234.85  -68082.1553 156019.59
## 2022.1205     62406.9117 -10902.1584 135715.98  -49709.6359 174523.46
## 2022.1233     35121.6840 -38230.3028 108473.67  -77060.4991 147303.87
## 2022.1260     65299.7387  -8095.1397 138694.62  -46948.0415 177547.52
## 2022.1288     39619.6361 -33818.1089 113057.38  -72693.7028 151932.97
## 2022.1315     70614.1412  -2866.4453 144094.73  -41764.7182 182993.00
## 2022.1342     74535.3476   1011.9445 148058.75  -37908.9941 186979.69
## 2022.1370     87597.9135  14031.7188 161164.11  -24911.8723 200107.70
## 2022.1397     75786.9932   2178.0316 149395.95  -36788.1988 188362.19
## 2022.1425     68194.7862  -5456.9173 141846.49  -44445.7740 180835.35
## 2022.1452     75916.6319   2222.2112 149611.05  -36789.2586 188622.52
## 2022.1479     81443.1471   7706.0340 155180.26  -31328.0358 194214.33
## 2022.1507     62280.7175 -11499.0632 136060.50  -50555.7200 175117.16
## 2022.1534     70169.9855  -3652.4384 143992.41  -42731.6690 183071.64
## 2022.1562     84006.2302  10141.1879 157871.27  -28960.6035 196973.06
## 2022.1589     58604.5829 -15303.0532 132512.22  -54427.3924 171636.56
## 2022.1616     94772.9079  20822.7024 168723.11  -18324.1717 207869.99
## 2022.1644     79461.4486   5468.6983 153454.20  -33700.6977 192623.59
## 2022.1671     86858.4539  12823.1833 160893.72  -26368.7216 200085.63
## 2022.1699    101868.0472  27790.2806 175945.81  -11424.1203 215160.21
## 2022.1726     59046.8608 -15073.3775 133167.10  -54310.2615 172403.98
## 2022.1753     42743.4303 -31419.2553 116906.12  -70678.6096 156165.47
## 2022.1781     11779.0055 -62426.1031  85984.11 -101707.9147 125265.93
## 2022.1808     59730.5404 -14516.9669 133978.05  -53821.2231 173282.30
## 2022.1836     62139.7769 -12150.1050 136429.66  -51476.7929 175756.35
## 2022.1863     53716.9376 -20615.2947 128049.17  -59964.4016 167398.28
## 2022.1890     40596.5939 -33777.9647 114971.15  -73149.4778 154342.67
## 2022.1918     79801.8018   5384.9410 154218.66  -34008.9656 193612.57
## 2022.1945     64000.1714 -10458.9677 138459.31  -49875.2549 177875.60
## 2022.1973     78881.3802   4379.9870 153382.77  -35058.6683 192821.43
## 2022.2000     60838.3502 -13705.2733 135381.97  -53166.2840 174842.98
## 2022.2027     66916.3404  -7669.4894 141502.17  -47152.8427 180985.52
## 2022.2055     86192.1644  11564.1521 160820.18  -27941.5313 200325.86
## 2022.2082     59001.6016 -15668.5693 133671.77  -55196.5701 173199.77
## 2022.2110     69793.5830  -4918.7228 144505.89  -44469.0284 184056.19
## 2022.2137     55061.3675 -19693.0494 129815.78  -59265.6473 169388.38
## 2022.2164     85681.3951  10884.8908 160477.90  -28709.9868 200072.78
## 2022.2192     81212.1907   6373.6227 156050.76  -33243.5222 195667.90
## 2022.2219     82866.7381   7986.1300 157747.35  -31653.2695 197386.75
## 2022.2247     80221.3467   5298.7221 155143.97  -34362.9196 194805.61
## 2022.2274     89853.6192  14889.0016 164818.24  -24794.8698 204502.11
## 2022.2301     67382.0092  -7624.5778 142388.60  -47330.6665 182094.68
## 2022.2329     67574.6584  -7473.8746 142623.19  -47202.1682 182351.48
## 2022.2356     98925.2663  23834.8108 174015.72  -15915.6753 213766.21
## 2022.2384     90096.2987  14963.9440 165228.65  -24808.7221 205001.32
## 2022.2411    108084.2601  32910.0296 183258.49   -6884.8042 223053.32
## 2022.2438    104931.9710  29715.8880 180148.05  -10101.1012 219965.04
## 2022.2466    103934.8315  28676.9193 179192.74  -11162.2129 219031.88
## 2022.2493     72011.2374  -3288.4808 147310.96  -43149.7437 187172.22
## 2022.2521     41767.7903 -33573.7106 117109.29  -73457.0920 156992.67
## 2022.2548     47945.5437 -27437.7169 123328.80  -67343.2045 163234.29
## 2022.2575     99133.3281  23708.3311 174558.33  -16219.2505 214485.91
## 2022.2603     82492.6739   7025.9634 157959.38  -32923.6999 197909.05
## 2022.2630     85422.3875   9913.9867 160930.79  -30057.7462 200902.52
## 2022.2658     69615.7374  -5934.3308 145165.81  -45928.1211 185159.60
## 2022.2685     80901.3151   5309.6025 156493.03  -34706.2330 196508.86
## 2022.2712    104352.4880  28719.1539 179985.82  -11318.7146 220023.69
## 2022.2740     77375.5133   1700.5806 153050.45  -38359.3089 193110.34
## 2022.2767     44332.7225 -31383.7859 120049.23  -71465.6842 160131.13
## 2022.2795     56915.7854 -18842.2759 132673.85  -58946.1710 172777.74
## 2022.2822     96209.4520  20409.8606 172009.04  -19716.0193 212134.92
## 2022.2849     94315.6332  18474.5344 170156.73  -21673.3181 210304.58
## 2022.2877     61738.3847 -14144.1988 137620.97  -54314.0120 177790.78
## 2022.2904     66172.7359  -9751.3096 142096.78  -49943.0715 182288.54
## 2022.2932    107975.9088  32010.4239 183941.39   -8203.2747 224155.09
## 2022.2959     86422.5691  10415.6674 162429.47  -29819.9558 202665.09
## 2022.2986     96569.8391  20521.5432 172618.13  -19735.9929 212875.67
## 2022.3014    114584.3428  38494.6752 190674.01   -1784.7618 230953.45
## 2022.3041    110518.8472  34387.8303 186649.86   -5913.4956 226951.19
## 2022.3068     94408.6802  18236.3366 170581.02  -22086.8664 210904.23
## 2022.3096     79810.9652   3597.3172 156024.61  -36747.7509 196369.68
## 2022.3123     60800.6190 -15454.3110 137055.55  -55821.2325 177422.47
## 2022.3151     56936.9461 -19359.2435 133233.14  -59748.0066 173621.90
## 2022.3178     75902.6371   -434.7899 152240.06  -40845.3828 192650.66
## 2022.3205     53924.8288 -22453.8133 130303.47  -62886.2241 170735.88
## 2022.3233     28281.3034 -48138.5316 104701.14  -88592.7486 145155.36
## 2022.3260     39401.5199 -37059.4858 115862.53  -77535.4972 156338.54
## 2022.3288     78269.7967   1767.6425 154771.95  -38730.1517 195269.75
## 2022.3315    102202.1994  25658.9188 178745.48  -14860.6464 219265.05
## 2022.3342    112243.4113  35659.0264 188827.80   -4882.2981 229369.12
## 2022.3370    103021.2765  26395.8093 179646.74  -14167.2628 220209.82
## 2022.3397     79422.5818   2756.0544 156089.11  -37828.7537 196673.92
## 2022.3425     64362.9686 -12344.5971 141070.53  -52951.1296 181677.07
## 2022.3452     67857.0911  -8891.4909 144605.67  -49519.7361 185233.92
## 2022.3479     49865.4822 -26924.0943 126655.06  -67574.0406 167305.00
## 2022.3507     64502.4187 -12328.1303 141332.97  -52999.7662 182004.60
## 2022.3534    109423.7798  32552.2800 186295.28   -8141.0338 226988.59
## 2022.3562    114988.7673  38076.3387 191901.20   -2638.6417 232616.18
## 2022.3589    120689.4693  43736.1335 197642.81    2999.4982 238379.44
## 2022.3616     84164.7645   7170.5433 161158.99  -33587.7354 201917.26
## 2022.3644     59261.5608 -17773.5241 136296.65  -58553.4348 177076.56
## 2022.3671     23713.8265 -53362.1005 100789.75  -94163.6316 141591.28
## 2022.3699     62469.4536 -14647.2938 139586.20  -55470.4339 180409.34
## 2022.3726     89481.9981  12324.4519 166639.54  -28520.2858 207484.28
## 2022.3753     74822.8096  -2375.5139 152021.13  -43241.8377 192887.46
## 2022.3781     56428.4678 -20810.6113 133667.55  -61698.5100 174555.45
## 2022.3808    112944.2080  35664.3946 190224.02   -5245.0675 231133.48
## 2022.3836    121641.8678  44321.3416 198962.39    3390.3275 239893.41
## 2022.3863    105277.1198  27915.9022 182638.34  -13036.6526 223590.89
## 2022.3890    105531.8358  28129.9483 182933.72  -12844.1359 223907.81
## 2022.3918     82200.7307   4758.1946 159643.27  -36237.4076 200638.87
## 2022.3945     71058.6000  -6424.5633 148541.76  -47441.6723 189558.87
## 2022.3973     58370.0468 -19153.7225 135893.82  -60192.3270 176932.42
## 2022.4000     82669.1685   5104.8145 160233.52  -35955.2743 201293.61
## 2022.4027     79047.7052   1442.7877 156652.62  -39638.7741 197734.18
## 2022.4055     90190.5623  12545.1025 167836.02  -28557.9211 208939.05
## 2022.4082     74833.3011  -2852.6799 152519.28  -43977.1541 193643.76
## 2022.4110     64236.6242 -13489.8568 141963.11  -54635.7705 183109.02
## 2022.4137     47357.4291 -30409.5309 125124.39  -71576.8727 166291.73
## 2022.4164     34687.0353 -43120.3825 112494.45  -84309.1415 153683.21
## 2022.4192     18993.7757 -58854.0789  96841.63 -100064.2439 138051.80
## 2022.4219     30017.0406 -47871.2299 107905.31  -89102.7897 149136.87
## 2022.4247     51039.8882 -26888.7772 128968.55  -68141.7207 170221.50
## 2022.4274     73275.0192  -4694.0202 151244.06  -45968.3365 192518.37
## 2022.4301     76760.2535  -1249.1390 154769.65  -42544.8169 196065.32
## 2022.4329     75586.3048  -2463.4199 153636.03  -43780.4484 194953.06
## 2022.4356     73160.0867  -4929.9494 151250.12  -46268.3174 192588.49
## 2022.4384     51927.4592 -26202.8674 130057.79  -67562.5640 171417.48
## 2022.4411     54988.4727 -23182.1237 133159.07  -64563.1378 174540.08
## 2022.4438     81228.4608   3017.6153 159439.31  -38384.7054 200841.63
## 2022.4466     84948.4289   6697.3550 163199.50  -34726.2613 204623.12
## 2022.4493     93214.7386  14923.4570 171506.02  -26521.4440 212950.92
## 2022.4521     84892.8457   6561.3770 163224.31  -34904.7977 204690.49
## 2022.4548    102813.0100  24441.3749 181184.65  -17046.0626 222672.08
## 2022.4575     51519.3555 -26892.4254 129931.14  -68401.1149 171439.83
## 2022.4603     55903.8275 -22548.0788 134355.73  -64078.0094 175885.66
## 2022.4630     66783.9704 -11708.0408 145275.98  -53259.2015 186827.14
## 2022.4658     49247.3183 -29284.7772 127779.41  -70857.1573 169351.79
## 2022.4685     51382.0940 -27190.0654 129954.25  -68783.6541 171547.84
## 2022.4712     79125.2720    513.0691 157737.47  -41101.7173 199352.26
## 2022.4740     69664.2673  -8987.9587 148316.49  -50623.9320 189952.47
## 2022.4767     82218.9795   3526.7509 160911.21  -38130.3987 202568.36
## 2022.4795     87666.5995   8934.3884 166398.81  -32743.9265 208077.13
## 2022.4822     97080.5068  18308.3336 175852.68  -23391.1360 217552.15
## 2022.4849     96803.8612  17991.7462 175615.98  -23728.8674 217336.59
## 2022.4877    101924.3145  23072.2779 180776.35  -18669.4689 222518.10
## 2022.4904     90913.6458  12021.7077 169805.58  -29741.1616 211568.45
##create forecast and actual data line together, create overlap plot
#red line deviates from the black peaks and bottoms
ts.plot(turbine_tsi, fitted(fit_AR3), gpars=list(col=c("black","red")))

#fit the original line well, pretty good

Create matrix of covariates for next 5 time periods

xdat <- c(5.73, 4.03, 3.88, 5.01, 4.51)
xdat1 <- matrix(xdat, nrow = 5, ncol = 1, byrow = TRUE)

xregmat = day_turbine1$wind_speed

##Re-run model with ARIMA and produce forcast for next 5 days

fit_AR3_v2 <- Arima(turbine_tsi, xreg = xregmat, order = c(2,1,1))
forecast(fit_AR3_v2, xreg = xdat1, h = 5)
##           Point Forecast     Lo 80     Hi 80     Lo 95     Hi 95
## 2020.2466       95691.92 75056.868 116326.97 64133.332 127250.51
## 2020.2493       45254.71 17471.239  73038.17  2763.559  87745.85
## 2020.2521       38432.54  7658.566  69206.51 -8632.190  85497.26
## 2020.2548       67648.10 35599.034  99697.17 18633.283 116662.92
## 2020.2575       53040.16 20398.333  85681.98  3118.796 102961.51
autoplot(forecast(fit_AR3_v2, xreg = xdat1, h = 5))